BACKGROUND OF THE INVENTION

1. Field of the Invention:

The present invention relates generally to the field of propulsion systems. Moro specifically the present invention relates to a uniform shape-shifting material that changes its mass distribution in a radial direction at particular angular arc segments due to an electromagnetic field acting upon the angular arc segments. In all of this specification, the word “ bulge” is commonly used and it shall equally be interpreted as a “depression”, since a bulge can occur in a radial direction toward and away from the center of rotation, respectively.

When a mass distribution is rotating in a dynamically and statically balanced state and rotating in a fixed frame member of reference, no wobble occurs in the frame member of reference. If the mass distribution is disrupted and an imbalance occurs, a wobble becomes evident in the fixed frame member of reference, and should the frame be free to move within the space defined by the fixed frame member of reference, then, the center of mass and the mass distribution will rotate in relation to one another about some barycenter point in the fixed frame member of reference. Should the wobble be controlled in angular span and time, relative to a non-rotating frame of reference, A, then, the wobble can become impulses directed in the same fixed direction in the fixed frame member of reference, A. In an ordinary rotating mass with an oscillating mass distribution, the barycenter, B, varies in radial position and also rotates as a varying mass distribution rotates. The motion of such a configuration is generally restricted to a multi-pointed trajectory as the barycenter moves back and forth from the equilibrium mass distribution to the offset mass distribution as it rotates. The barycenter B, tends to move toward the direction of greater mass distribution. However, in this invention, if this tendency for the barycenter B, to move is unitary, in that, no motions of the barycenter B occur in any other dimension except for a fixed linear radial and angular direction aligned with impulsive wobble, then there exists a continuous tendency for the barycenter B to move in the direction of the linear momentum change ΔM’s direction.

Although such a propulsion system will be biased due to the rotation of its parts, simply using two or balanced pairs of the apparatus generates an unbiased linear propulsion.

As shown in FIGURE 11, in a governor, with a mass M, that is lifted by angular rotations of a shaft member against its gravitational force. Mg, the lifting force F, is dependent on the vertical height, h, of the mass M, from the pivot of rotation. Thus, the force needed to lift the mass against gravity is dependent on the angle α, between the arm of the governor that rotates and holds the mass M, and the vertical axis of rotation, and on the angular speed to, of the rotation. The general relation between the two follows the relation:

It is clear that to get to the horizontal plane α = 0, from a fixed angular orientation of the rotating arm requires a tremendous speed of rotation, ω, since, the ratio above varies exponentially, as The fact that a governor can lift large masses that rotates, gives us an idea of how powerful centripetal forces can become.

Suppose a rotating disc member is connected to a motor shaft member that rotates uniformly with angular rotational speed, to, with uniform torque in a fixed frame of reference, A, comprising the apparatus of this invention. Suppose the disc member has shape-shifting material that is evenly distributed about a center of symmetry of the rotation and is dynamically and statically balanced about the shaft member to rotate uniformly at uniform angular rotational speed, at. Suppose, there is a fixed incremental span of an arc segment θ°, of the shape-shifting material, that is made to be a shape-shifting arc segment by means of an electromagnetic actuator mechanism, such as, a magnetic field, and an electric field. The actuator for an electric field can be a piezoelectric crystal, and for the magnetic actuator, a ferrofluid. The actuation occurs at the particular angular segment θ°, forming a very small arc that is fixed in relation to the frame, A.

Let the initial centroid radius of symmetry of a mass distribution δm of the shape-shifting arc segment be and let the mass distribution δm be actuated impulsively (very fast) to move a new centroid radius * The change in energy ΔE, of the mass 6m that is ejected from symmetry by the radial redistribution, changes its tangential velocity from an initial velocity V _t at radial symmetry radius R ₂ , to a final velocity V ₂ , at either a maximum or a minimum radius ± . This removes energy, from motor shaft member to keep the motion at constant angular rotational speed, ω.

The energy ΔE to move the mass δm radially from its initial rotational tangential velocity to its new rotational tangential velocity V ₂ , comes from the electromagnetic actuator. However, there is a sudden change in linear tangential momentum change — , of the moved rotating mass δm, is directed as an accelerative force to the radial orientation of the small arc segment θ°, of the moved mass, δm, in the frame, A. This Is the governor principle.

If the arc segment θ° is small enough, and the actuator is fast, the change in linear moment ΔM can be an impulsive force generated by the mass distribution δm of the shape- shifting arc segment that is directed to the arc, θ°.

In the governor example, assuming is the shaft radius (for purposes that become clear later), if the mass M. changes its radius, R ₂ , suddenly to a new radius R ₂ ± δ, the motor driving the governor must receive or donate the energy, to keep the mass M, at its new radius. Such an impulsive change on a governor’s rotating mass restricted only to a particular small angular orientation of its rotation, will generate a sudden wobble-force directed at that angular orientation, and this wobble-force, F, only acts on the shaft member of the governor in that angular orientation θ°, i.e., in the direction of the sudden change.

If one ensures that the during its entire rotation, the radial location of the mass M of the governor is unchanged everywhere except at the angular orientation θ°, then, there exists a continuous impulsive force of frequency ω, acting on the shaft member in the orientation θ°.

The oscillating mass distribution of mass distribution 6m, can be perpetuated as linear pulsed oscillations in the direction of the arc segment θ°, Then, the net motion of the entire apparatus will be in a linear direction either toward or away the arc segment θ°. This is shown in FIGURE 1, where, the radial-change in acceleration over the arc segment θ°, has been exaggerated for explanation, and the direction of the force, F, is away from the smaller radius, R ₂ - δ.

If such an imbalance is restricted in one dimension only, i.e., a perpetual imbalance in that direction, then, the apparatus will have the same perpetual tendency to wobble in that direction only. Then, all the wobble energy is directed in that direction, and the apparatus will move impulsively in that direction.

The present invention uses a disc member, containing a symmetric and dynamically balanced shape-shifting mass distribution of a shape-shifting material at a fixed radius, R ₂ , to generate linear impulses, or “pulses” by shifting the mass distribution of the shape-shifting material in a fixed angular direction of the fixed frame member of reference of the apparatus to a new radius, R ₂ + δ. The shape-shifting is achieved by using a shape-shifting material that can be directed by an electromagnetic impulse, such as an electric field and a magnetic field to “wobble” linearly in a preferred angular arc segment θ°, of the rotation, that is fixed in direction in the space, S, defined by tiie fixed frame of reference A, of the apparatus. The shape-shifting arc segments used by the invention responds to electromagnetic stimuli (i.e., electric and magnetic stimuli), to shift shape-shifting material, to an imbalance in the preferred angular arc segment θ°. only. Advantageously, the shape-shifting material; can be any material that responds to electromagnetic fields. In such a case, the shape-shifting material can be made from solid materials and from liquid materials. The solid materials can be chosen from piezoelectric materials, nitinol materials that respond to changes in temperature (electromagnetic spin moment changes in their structure) and electromagnetic fields. Advantageously, the shape-shifting materials can also be magnetohydrodynamic fluids that change shpe due to electric and magnetic fields imposed on them.

By “electromagnetic stimuli” is meant either, magnetic-stimuli, or electric-stimuli, and the stimuli can also be generated by both fields. An eccentric mechanical trajectory is not needed to guide the eccentric flow of the matter distributions used in the present invention. The apparatus of the present invention does not go into an imbalanced state as the stimuli are generated and induced to shift the mass distributions of the shape-shifting material. Since the shape-shifting is designed like a tidal-force acting on particular shape-shifting arc segments of the apparatus in a given shape-shifting arc segment pointing in a fixed direction of the space. The shape-shifted mass distribution is contained in a disc member that rotates with the shaft of motor. The shape-shifting material can also be the same material that forms the shape-shifting arc segments. The entire disc member can also be made from the shape-shifting material. The apparatus thus created, does not go into rotational imbalance, but goes into a linearly directed imbalance toward the preferred angular arc segment θ°, since the flow of material is directed in space at this particular direction in the space of on the rotating mass distribution. The imbalance caused at angular arc segment θ°, become a directed impulse-wobble that is a motive force. However, there is a generated imbalance in the centripetal force F, only in the direction of the shape-shifting angular arc segment θ°, of the apparatus.

The disc members used can be made with shape-shifting material contained within it that responds to one of the electromagnetic fields, The centripetal force imbalance, F _θ generated by the imbalance act like tidal forces in a similar manner to a gravitational field of the Moon, causing a tide on Earth where there is a fixed tidal bulge located only in the direction of the centers of the Earth and the Moon, caused by external gravitational forces of the Moon.

The shape-shifting materia! (like the oceans of the Earth), rotates and passes through a shape-shifting arc segment causation of the apparatus, at a frequency of rotation to, of the encoded motor, multiplied by the number of such shape-shifting arc segments. The rotational range is any desired angular speed that can be achieved by the apparatus. Due to physical limitations, the shape-shifting arc segments can be limited in number of are segments distributed around the disc member. However, it is possible to use either a magnetic fluid or a piezoelectric material for an infinitely gradated rotating shape-shifting material.

An electromagnetic tidal force E _HM is applied to one or more of shape-shifting arc segments at a particular angular portion of the disc member to cause either radial depression R ₂ — δ, or a radial bulge R ₂ + δ, of the shape-shifting material, The act of radial redistribution of the mass shape shape-shifting material in the particular actuated radial direction, is very fast and can vary from 50kH to 27 MHz (megahertz) frequency, while the angular speed ω, is at a far lower frequency in the range of 0.5kH to 500kH (kilohertz) regions. The rapid displacement of the shape-shifting arc segments in the radial directions is designed to do work by displacing the mass distribution of the shapeshifting material in the direction of either an increasing centripetal forces as its radial flow increases its tangential velocity vector, or a decreasing centripetal force, as its radial flow decreases its tangential velocity vector. There is a sudden change in linear tangential momentum change, ΔM = δm(V ₂ — V1), of the moved rotating mass δm, is directed perpendicular to the radial angular orientation of the small arc segment θ°, of the moved mass, δm, and since the mass distribution is held from flying off, as it changes its radius, it generates an accelerative force we call the centrifugal force.

There are two electromagnetic forces that can be used to actuate the shape-shifting: a) An electric field that imparts an electric potential difference φ _E , on the shape- shifting material of the disc member. b) A magnetic field that imparts a magnetic potential difference on the shape- shifting material of the disc member,

The shape-shifting arc segments material passing a region of actuation where it is forced by either a magnetic potential difference φ M, or an electric potential difference φ _E , to either bulge, or depress, to a different radius from its rotational radius of symmetry.

In all of this specification, the word “bulge” is commonly used and it shall equally be interpreted as a “depression”, since a bulge can occur in a radial direction toward and away from the center of rotation, respectively.

An eccentric shape-shifting material rotating with a shaft member will cause a wobble in a frame member of reference, A, that Is rotating the shaft member. The wobble is a result of offset centrifugal and centripetal forces acting on the rotation. If such a wobble is caused to locate in one direction of the frame member of reference, A, then one can conceive of an approximation to a mathematical step-impulse-ftinction that causes a directed wobble force in only one direction relative to a frame member of reference, A. If now, the wobble is made with motion vector in a specified direction, it is no longer a wobble but a directed force, F _θ , that has an oscillation with frequency ω, in A in the direction of the arc segment, θ°. This frequency to, aligns with the momentum change forces, and will reinforce and diminish this force in an oscillatory' manner, if the mass distribution of the shape-shifting material is made symmetric at all points removed from the wobble-cycle, then the offset in radial centripetal forces, F, at the maximum and the minimum bulge will result in a net force F _e , in the direction of the bulging (contracted) arc segment θ°,

This can be achieved in two ways. In (a) above, an electric potential difference φ _E , can act on the shape-shifting arc segment of the disc member to change its radial shape at a particular angular orientation to change the centripetal forces acting in that radial direction only. In (b) above, a magnetic potential difference can act on the shape-shifting arc segment of the disc member to change its radial shape at a particular angular orientation to change the centripetal forces acting in that radial direction only, Both angular actuations can be made as small as possible to achieve an impulse flow in the selected angular orientation only.

Advantageously changing in the angle of activation of the impulse generates a steering means for the apparatus.

There two ways to change the mass distribution of the shape-shifting material of the disc member:

A) Changing the mass distribution of the shape-shifting arc segment of the disc member radially. This requires the shape shifting mass of the shape-shifting arc segments to be moved radially by an activating electromagnetic force.

B) Changing the circumferential mass distribution of the shape-shifting arc segment of the disc member. This requires the shape shifting mass of the shape-shifting arc segments to be moved circumferentially by an activating electromagnetic force.

In both cases, the shape-shifting arc segments have shape-shifting materials that can be moved by an activated shape-shifting arc segment at a particular angular arc segment θ° that determines the direction of the forces thus generated by centripetal forces acting on the shape- shifting materials.

Prior art uses piezoelectric crystal motors to prescribe various ways to generate motions using the programmed oscillations of a piezoelectric crystal when actuated by an electromagnetic field. There are no propulsion systems that provide a propulsive linear force in Space by mere rotations. Rotations and wobbling in Space S, can be obtained by the eccentric behavior of rotating members* Linear and orbital propulsion can be achieved with combustible fuels, solar wind, and ion propulsion engines. Propulsion can also be achieved using a passive means such as gravitational sling of a spacecraft in orbit around a gravitating mass. No prior art demonstrates a shape-shifting apparatus that relies on rotations to generate propulsion forces.

It is known that centripetal forces vary with the radius of rotation. This feet leads to eccentrics that can generate a rotational torque difference about a center of rotation held between one part of a rotating member at a given radius of rotation and its other parts at different radii of rotations. This is just an imbalance in rotational torque that results in torsions on the shaft of the rotating apparatus and can lead to offsets in rotational orbits. However, rotational moments cannot do work if they are orthogonal to the motion of a rotating mass that generated them.

Patent WO 2016/101062 shows such an apparatus using dark matter. It depends on mechanically rotating a mass on a mechanical eccentric trajectory using a mechanical link to rotate the mass along the eccentric trajectory and generating dark matter energy. The mass wobble rotates with the shaft on the trajectory and then goes into the eccentric portion of the trajectory to generate a difference in centrifugal forces on the rotating shaft leading to orbital rotation variations. If a craft is in orbit and the eccentric mass is rotated at the right moment, It can offset the craft and cause a deviation of orbits using the wobble. However, this is not a propulsion system that can perform linear motions. Thus, the forces generated are periodic with the rotation with net zero work, This creates a lot of imbalance and possible wobble on a spacecraft.

In the present invention, no such predefined mechanically linked trajectory about a center with an eccentric portion for a rotating mass member is required. The gravitational sling, used on orbiting spacecrafts, is an example of radial change of mass distribution of a spacecraft in an orbit due to an active field external that changes to sling the craft tangentially in the orbit. This orbital sling depends on the orbital gravitational change in rotational kinetic energy of the spacecraft and its balance with the gravitational field attracting the spacecraft radially to an orbital path. The escape velocity is the tangential velocity on the orbit that is required for a given gravitating body to release the spacecraft Into an elongated elliptic orbit, and finally into an almost linear trajectory that i s desired . One can think of this apparatus as equivalent to a gravitational-tidal force acting on the apparatus from within it (the actuating electromagnetic field). In 3D environments, propulsion requires multi-thrusters propelled by explosive gases generating a reactive force to propel a craft. For example, in submarines and in airplanes, control surfaces are needed to manipulate a craft that provide directional thrust. A propulsion system using encoded motors that creates a directional thrust that can be controlled without manipulating surfaces of a craft for a given direction of 3D space is of importance,

In the present invention, a uniform shape-shifting rotating disc member changes its mass distribution at a particular angular arc segment θ°, in a radial direction due to an electromagnetic field acting upon that angular arc segment θ° * No eccentric mechanical trajectory to guide a mass is required* The present apparatus does not go into an imbalance, since the shape-shifting is like an internally generated tidal force acting on the shape-shifting mass distribution of a disc member. The disc member has a multiplicity of shape-shifting arc segments that can respond to electromagnetic fields acting on them. Each shape-shifting arc segments passes a shape-shifting region of the apparatus at a frequency co, of rotation of the encoded motor, multiplied by the number of such arc segment The shape-shifting arc segments cause the shape-shifting material to change its radial distribution on the disc member causing a directed impulse wobble. The rotational range is 40 revs per second, to over 500 revs per second. Due to physical limitations, the shape-shifting arc segments are limited in the number distributed around the disc member. The shape-shifting arc segments pass the region of change at a frequency of ncu kH, where n, is the number if shape-shifting arc segments possible on the disc member. An electromagnetic tidal force is applied to one or more of shape-shifting arc segments at a particular angular portion of the disc member ’s perimeter to cause a depression or a bulge of the shape-shifting material. The act of radial distribution of the mass in the radial direction is very fast and is in the 500kH to 27 MHz (megahertz) frequency, while the rotational speed co, is much slower with a frequency in the 2KH to 50KH (kilohertz) regions* The rapid displacement of the shape-shifting arc segments is designed to do work by displacing the mass distribution in the direction of its changing centripetal forces as its radial flow changes its momentum and its velocity*

The shape-shifting arc segments material passing this region of actuation is forced into this bulge by electromagnetic forces. In all of this specification, the word “bulge” is commonly used and it shall equally be interpreted as a “depression”, since a bulge can occur in a radial direction toward and away from the center of rotation, respectively. “Electromagnetic” can be interpreted as either an electric potential φ _E , or a magnetic potential since the two forces are interdependent and when in motion, a shape-shifting materia] that responds to either will generate the other force.

In all of the foregoing, a shape-shifting arc segment can be made from the shape-shifting material itself. For economy, the shape-shifting material can be made from massive elements such as metals, ceramics and other suitable materials that can be configured to shift their mass distributions radially using any electric and any magnetic means and any combination of both fields. The most important aspect of the invention is that the shape-shifting arc segment causes a radial-change in the mass distribution of the shape shifting material resulting in an impulsive force that generates a motive force.

In its various configurations, the apparatus can be made from fluids that are rotated by electric motors, magnetic motors and by magnetohydrodynamic forces. The apparatus can be powered by solar cells that provide the propulsion energy to the shape-shifting materials.

It is thus an object of this invention to provide a means of generating a directed propulsion using electromagnetic fields and a shape-shifting material to generate an impulsive centripetal propulsive force.

It is another object of this invention to provide a means of directed propulsion using magnetic fields and a shape-shifting material to generate an impulsive centripetal propulsive force.

It is another object of this invention to provide a means of directed propulsion using electric fields and a shape-shifting material to generate a propulsive force.

It is yet another object of the present invention to provide for an apparatus that uses magnetohydrodynamic forces to convert rotary motion to a linear propulsive force to propel a craft.

It is yet another object of the present invention to provide such an apparatus that can use electric and magnetic fields to deflect rotating flexible metallic string materials to change their mass distribution and generate centripetal propulsion.

It is yet another object of the present invention to provide for an apparatus that converts rotary motion to a linear propulsion system.

It is another object of the invention to provide an apparatus with a shaft that is powered by one of, solar energy, a battery pack, and an engine, to produce a directional propulsive force for a spacecraft in Space S. It is another object of the invention to provide an apparatus that can be used to propel an aircraft in a 3-dimensional space.

It is another object of the invention to provide an apparatus that can be used to propel an aircraft in a 3-dimensional space without the need for lifting airfoils.

It is another object of the invention to provide an apparatus that can be used to propel an aircraft in a 3 -dimensional space without the need to use steering vanes,

It is another object of the invention to provide an apparatus that can be used internally in a submarine without contacting water to propel a submarine in a 3-dimensional ocean without the need to use steering vanes. it is another object of the invention to provide an apparatus that Can be used internally in a submarine to reduce any noise pollution,

It is another object of the invention to provide an apparatus that can be used internally to propel a flying vehicle that can also be a road vehicle.

It is a further object of the invention to provide for an apparatus that can be scaled radially to provide for larger propulsive forces in a gravitationally free environment.

It is another object of the invention to provide an apparatus that can be powered by a motor to produce a directional propulsive force.

It is a further object of the invention to provide for an apparatus that can provide a propulsive force that can act against a gravitational field.

It is another object of the invention to provide an apparatus that can be used internally to reduce any noise pollution in a submarine.

It is finally object of the invention to provide an apparatus that can be used internally to reduce any noise pollution in an aircraft

SUMMARY OF THE INVENTION

The present invention accomplishes the above-stated objects, as well as others, as may be detenu ined by a fair reading and interpretation of the entire specification*

The present invention relates to a uniform shape-shifting rotating disc member that changes its mass distribution at a particular angular arc segment in a radial direction due to an electromagnetic field acting upon that angular arc segment. No eccentric mechanical trajectory to guide a mass is required. The present apparatus does not go into an imbalance, since the shape-shifting is like a tidal force acting on the shape-shifting mass distribution of a disc member. The disc member has a multiplicity of shape-shifting arc segments that can respond to electromagnetic fields acting on them. Each shape-shifting arc segments passes a shape- shifting region of the apparatus at a frequency of rotation of the encoded motor multiplied by the number of such arc segment. An electromagnetic tidal force is applied to one or more of shape-shifting arc segments at a particular angular portion of the disc member 's perimeter to cause a depression or a bulge of the shape-shifting material. The act of radial distribution of the mass in the radial direction is very fast and is in the 500kH to 27 MHz (megahertz) frequency, while the rotational velocity is much slower with a frequency in the 2KH to 50KH (kilohertz) regions. The rapid displacement of the shape-shifting arc segments is designed to do work by displacing the mass distribution in the direction of its increasing centripetal force as its radial flow increases its velocity.

The shape-shifting arc segments material passing this region of actuation is forced into this bulge by electromagnetic forces. In all of this specification, the word “bulge” is commonly used and it shall equally be interpreted as a ‘’depression”, since a bulge can occur in a radial direction toward and away from the center of rotation, respectively.

A good model for the present invention is the tidal force generated by the Moon on the Oceans, he following table shows the comparative model:

It is easy to compare the two models using TABLE 1.

The gravitational tidal force of the Moon (field source) on a rotating Earth (rotating disc member) with shape-shifting Oceans (shape-shifting arc segments), can be imagined to be acting against the gravitational tension of the Earth (internal molecular forces) holding a shape- shifting Ocean to the rotating Earth. Thus, one can compare this to a shape-shifting material (Ocean) that has tensile strength due to its atomic structure holding its parts together (gravity) on a rotating disc member (Earth). Hence, in the analogy, the material's tensile strength of the disc member is equivalent to the Earth's gravitational field holding its Oceans together, and the shape-shifting material can be compared to the Ocean, The shape-shifting Ocean arc segments in a tide on a rotating Earth (disc member) are equivalent to the shape-shifting arc segments of the present apparatus on a rotating disc member.

In the present invention, the topological bulging “or contraction” of the shape-shifting arc segments does not rotate with the disc member, Like the tidal bulge, the bulging “or contraction” of the shape-shifting arc segments is designed to remain at the same small relative angular location as the forces that create it For simplicity we will only deal with bulging of the disc member, however, the same effect in reverse can be obtained by a depression of the disc member during rotations.

Advantageously, the disc member can be made with shape-shifting materials using stacked piezoelectric crystal actuators that oscillate with electric fields particular manners to keep their mass elements in the same angular orientation during rotation. A piezoelectric crystal can be made to oscillate in a variety of directions and shapes depending on the loading of its oscillation frequencies in a circuit When the directed impulses are actuated with a magnetic field the same effect can be achieved with a ferromagnetic fluid comprising the shape-shifting material in the disc member. Thus, one can imagine the shape-shifting arc segments as countering any rotational vectors as their radial location increases and decreases to gain a net displacement in a radial direction that is fixed in the reference frame member, O, This can be done by programming the motions to perform the motion relative to the rotation rate of the disc member.

When the massive elements of such a shape-shifting material arrive at a specific angular orientation during rotation, its mass distribution can be changed to a mew radial location and then allowed to go back to its relaxed symmetry state as the next shape-shifting force is applied to repeat the cycle tp the next segment of the disc member. The tidal bulge of the Earth is ever present along the line joining the Earth’s center to the Moons center, where the Moon’s gravitational field is applied* In a similar manner, the bulge of the shape-shifting disc member is ever present in a preferred angular direction in the rotation plane of the disc member where an electromagnetic field is applied. The electromagnetic field causing a bulging of the disc member is equivalent to the Moon’s gravitational field causing a bulging of the Ocean. The bulge of the shape-shifting Ocean arc segments is an equivalent model to the bulge of the shape-shifting arc segments of this invention.

In the present invention, the force that makes the bulge on the disc member is generated by an electromagnetic field causing the disc member ’$ shape-shifting material to be distributed either away from the disc member ’s center or toward the disc member ’s center. In the Earth- Moon-Ocean model, the force that makes the tidal bulge Is generated by an attractive gravitational force between the Oceans and the Moon, also pointing in a radial direction of the rotating Earth towards the tidal bulge.

Note that to keep the Earth-Moon system in a stable orbital trajectory, the centrifugal forces generated by the rotating Earth balance must balance the gravitational tensile ray between the Moon and the Ocean's tidal bulge on the rotating Earth,

Note that centrifugal and centripetal forces generated by the rotating disc member, balances the electromagnetic tensile ray acting in the shape-shifted arc segments of the rotating disc member. In the frame member of reference common to the Earth-Moon system, the gravitational tensile ray between the Moon and the Earth remains constant and spread over a small angle. As the Earth rotates, the bulge always points in the same line joining the Moon and the Earth,

The shape-shifting arc segment material’s tensile ray between the center of the disc member and the applied field, E, that causes the bulge is also directed at a particular angle, θ°, in their joint frame member of reference, O. In the present invention, the Electromagnetic source that produces the “tide” (bulging of the shape-shifting arc segment) is also external to the disc member ’s shape-shifting arc segments. The Moon is not present inside of the Earth to produce its "tides”. It is external. In the present invention, the Electromagnetic source that produces the “tide” (bulging of the shape-shifting arc segment) is also external to the disc member ’s shape-shifting arc segments but acts internally on the disc member 's shape-shifting arc segments. Changing this electromagnetic field is the equivalent of changing the Earth’s gravitational field’s hold on the tide. By changing the electromagnetic field of the shape- shifting arc segments, one can change the radial distribution of a shape-shifting material as a bulge on the disc member, and the shape-shifting arc segments are allowed to increase or decrease their radial mass distribution relative to the rotating the disc member in the given direction of choice. By changing the Earth’s gravitational field, one can change the radial distribution of mass of the Ocean’s tidal bulge and this will increase or decrease their radial tide’s mass distribution relative to the rotating Earth, However, it must come to notice that changing the gravitational of the Earth or the Moon should result in a relative change of radial orbits and hence a force of motion away from their centroid of rotation is created. This is an increase in Torque if the rotational speed of the disc member is constant.

In the apparatus, there Is no external orbiting forces acting, other than those generated by the rotation of the disc member parts and the actuator means. The angular rotational speed of any point on the bulge remains constant over time relative to the applied angle of activation of the bulge. The bulge is made radially and so the mass elements of the shape-shifting arc segments are continuously subject to the same shape of the bulge, the bulge remains independent of the rotation. Thus, all the mass elements of the disc member must pass through a bulging process. Therefore, just as the Ocean tidal wave has little or no rotational vectors (apart from miniscule gravitational drag and miniscule frictional drag) from the rotating Earth acting upon it in a tangential direction of the rotational disc of the Earth, the bulge of the shape- shifting arc segments is static and has little or no rotational vectors acting upon it, apart from miniscule electromagnetic drag in the tangential direction of the rotating disc member. This bulge (the shape) does not rotate with the motor shaft but it generates a tensile force that tends to puli the masses toward the top of the tidal direction as massive elements pass through it. If there is nothing holding the shaft back, there will be a reaction to the action of radial deviation that tends to shift the shaft back to symmetry with the bulge, The centripetal forces of the shape-shifting arc segments passing through the bulge are different from those of the “unbulged”-areas. In-fact there is an overall balance of such forces around the shaft, except at the bulge, which generates a directional difference of forces, F, in that particular angular orientation of the rotation only. This difference in forces, F, is not countered by the reaction to the bulging forces. It is a real force. The masses on the entire disc member will always be in perfect rotational balance, just as the Earth is always in rotational balance even with the tidal bulge with respect to time. As long as the centripetal force of imbalance is greater than the force exerted by the reaction on the shaft and, if the imbalance generated on the barycenter is nullified by a symmetric pair of disc members cn the same frame, then, there will be a net force acting on the apparatus In the direction of the bulge, and this can be used for propulsion.

In the Earth-Moon model, the centripetal radial forces that hold them together to a nearly circular orbit that balances the centrifugal forces that the Earth's tide creates. Unlike the Earth-Moon model, an electromagnetic tidal force has been created on the disc member that has no external source of rotation centrifugal force that counters and offsets the centrifugal forces generated by the bulge about an external center (like the center of the orbits of the Earth Moon system). Hence the apparatus will always have a net freedom to move along the moment ray generated by the change in velocities of the displaced mass distribution of the shape- shifting arc segment as its matter progressively migrates in the direction of θ°, and generates a motive moment ΔM. There is an attraction force of the rotating disc member to migrate towards the direction of the continuous flow of its matter in the direction of the linear moment difference. This force, F, causes a net movement of the entire apparatus in that direction. One can imagine that the bulge of material due to the electromagnetic energy is like an external gravitational field imparted on the mass of the shape-shifting arc segments in a continuous manner, but unlike the Earth and the Moon orbiting each other and held at “fixed" orbits by centrifugal forces, there is no force stopping the apparatus from migrating in the radial direction of the mass flow.

When either a compressive force (pressure), or, a tension force is applied to a shape- shifting material such as a ceramic piezoelectric crystal, and a ferromagnetic fluid, a magnetic potential φ , develops across the shape-shifting material surfaces generated by an offset of its molecules' ionic structure from a balanced state. Conversely, when one of the electromagnetic fields is applied to the shape-shifting material, the shape-shifting material responds by cither extending radially, (elongating) or contracting radially, generating a force.

If a piezoelectric material is used for shape-shifting, there is a longitudinal mode effect (deformation colinear electric potential φ _E and applied potential are linear,) and a transverse mode effect (deformation is perpendicular to the potential), A cycle of both modes can be designed to cause specific oscillations of the material’s dimensions by manipulating an electromagnetic field applied to the crystal surfaces to allow a defined shape of the shape- shifting material to be achieved. This defined motion occurs in three states of the shape-shifting material. A relaxed normal state, a contracted state, and extended state.

Similarly, when either a compressive force (pressure), or, a tension force is applied to a magnetic shape-shifting material, a resistive electromagnetic field develops across the material surfaces generated by an offset of its molecules’ ionic structure fiom a balanced state. Conversely, when an electromagnetic field is applied to the magnetic shape-shifting material, the magnetic shape-shifting material responds by extending (elongating) and contracting, generating a force* When a disc material member comprises, a magnetic fluid, made up of particles of magnetic materials, such as iron filings, is held between two discs, the rotation of the discs can generate a rotation of the disc material member. This rotation imparts a centripetal force F on the shape-shifting disc material. A sudden direction change in the radial mass and density distribution of a disc material member can generate a loss or gain of momentum of the disc material member in the change direction, causing either a deceleration or an acceleration of the apparatus. The change has to occur in a given fixed angular orientation to the general space of rotation.

When a rotating magnetic fluid made up of magnetic particles that are suspended in a fluid suddenly encounters a magnetic field along a segment of a cord of the rotational disc material member to impede the radial outward flow of the magnetic particles in a particular angular segment of rotation at radii that are now less than the original rotation radius of the magnetic particles, a sudden change in momentum is generated that must be transferred by the fluid to the frame A, The centripetal forces are lowered by the smaller radial flows, and the deceleration of the magnetic particles in the segment of the cord will transfer the momentum of the magnetic fluid particles to the magnetic field at the radial disposition of the segment of the cord. A motor supplies rotational energy to the magnetic particles in the first place. This motor energy of the rotation is transferred to a sudden linear motion along the magnetic field on the segment of the cord and causes the magnetic particles to flow along the segment of the cord along which the magnetic field is applied. Note that the magnetic field force is attractive to the magnetic materials, and this attractive energy is additive to the motor rotational energy acting on the magnetic particles encountering the magnetic field. The rotational motion now becomes a linear motion on the segment of the cord along the magnetic field.

For convenience if the magnet is placed on a segment of the cord defining a small angular orientation of the disc member, the disc member’s shape-shifting material will be attracted to the cord away from the larger rotation radius. In the region of the applied magnetic field, the magnetic particles are imparting a decreasing centripetal force on the magnetic field along the radial direction until they reach the center of the segment of the cord perpendicular to the radial direction, and continue to do so but with an increasing centripetal force on the magnetic field along the radial direction until they reach the end of the segment of the cord. Thus, the motor continuously transfers momentum to the magnetic field in the direction of the segment of the cord. Essentially, one can think of the process as a thruster (pressure) of magnetic particles hitting the magnetic field in the direction perpendicular to the entry segment of the cord.

In both the magnetic and non-magnetic shape-shifting materials, a shape-shifting occurs resulting in dimensional changes of the material in preferred directions. As such I will call such materials “shape-shifting materials”. Any rapidly shape-shifting material can be used to construct the apparatus 10 and its components.

In genera], when a shape-shifting material is made from piezoelectric crystals, it's response to an electric field is caused by an external electromagnetic field that changes its center of charge of the generally neutral ionic structure of the material, This induces a reorganization of the ionic lattice into a particular “poled” shapes* The “poling polarity” determines the behavior of the shape-shifting material. Magnetic poling is just as effective. When a ferromagnetic material is used, it has a magnetic moment that is inherent in the material that can be influenced by an external magnetic field. Shape-shifting materials go through a poling hysteresis loop (either an electrification and a magnetization loop) as they are activated, and then, relax.

In a similar manner, magnetic semi-sollds, magnetic fluids and piezoelectric crystals undergo the same process. White the foregoing description is with shape-shifting materials forming the disc member, nothing prevents one from using a disc member that can fluidly change shape by application of external fields that can influence the material. These include, electric, magnetic, and electromagnetic fields. Every aspect of the invention equally applies to all shape-shifting material. As such the shape-shifting technology implies any rapid shape- shifting material (micro-seconds response time) can be used to make the disc members of the foregoing description of the apparatus.

BRIEF DESCRIPTION OF THE DRAWINGS

Various other objects, advantages, and features of the invention will become apparent to those skilled in the art from the following discussion taken in conjunction with the following drawings, in which:

FIGURE 1 shows two disc-members with shape-shifting arc segments made from massive members containing a small shape-shifting material for moving the masses circumferentially to generate a radial-change in their mass distribution. FIGURE 2 shows two disc-members mounted on a frame member and powered by motors with a magnet placed in proximity to the disc member forming a segment of the cord that acts as the preferred angular shape-shifting arc segment of a ferromagnetic fluid within the disc members. The magnetic field acting along a segment of a cord of the disc member, attracts the magnetic mass distribution of the magnetic particles as they rotate in the disc member causing a change in their radial distribution.

FIGURE 3 shows an exploded view of the apparatus with a magnetic actuation disc member.

FIGURE 4 shows radial changes and in material flow as electromagnetic forces acting on magnetic shape-shifting material to re-distribute the mass of the magnetic particles in a ferromagnetic fluid in the disc member at a shape-shifting arc segment.

FIGURE 5 shows an enlarged disc member with the flow of ferromagnetic material along a an angular arc segment, θ°, of a segment of a cord of the disc member. The magnetic field EM causes a depression tidal force between the shrunk radius, R ₂ — δ and the original symmetry radius, R ₂ , generated on the angular segment θ° of the shape-shifting material to generating a linear motive force due to the deceleration (breaking) of the particles from their larger radius flow,

FIGURE 6 shows the magnetic field forcing the ferromagnetic fluid to flow toward the magnetic field and deviate from the circular flow causing the change in acceleration in the radial direction. The resulting forces cause a centrifugal impulse force • in the arc segment and energy is transferred to the magnetic field frame member from the shape- shifting arc segment.

FIGURE 7 shows two-disc members attached to an axle of a vehicle. The shape-shifting arc segments are made from electromagnetical ly active materials and subjected to applied electrical potentials φ _E , to change their shape. Brushes are shown to transmit the electric current flow from an electrical power source to the shape-shifting arc segments.

FIGURE 8 shows the disc member made from piezoelectric materials used as shape- shifting material.

FIGURE 9 shows the disc member with the radial configuration of the shaft member and the disc member.

FIGURE 10 shows a single circumferentially actuated shape-shifting arc segment. The actuated shape-shifting arc segment of a disc member is shown with a reduction in radius of the sector S1 S2 and the increase in radius of the sector S2S1 of a radial edge actuated disc member.

FIGURE 11 shows the centrifugal forces acting on a governor.

FIGURE 12 shows the centrifugal forces acting on two disc members that can be activated by electromagnetic impulses to increase the diameter of the disc member to change a directional centripetal force on the disc members.

FIGURE 13 shows a typical set up of the apparatus in a flying car chassis that can also defy gravity.

FIGURE 14 shows how such a flying car can be built with wheels incorporating the disc members.

FIGURE 15 show the typical configuration of a motor, the disc member, power source and controllers for a road and aerial vehicle.

FIGURE 16 shows the general relations of the disc members shape-shifting arc segments when actuated by an electromagnetic field with two sectors P _o and P1. P1 is shown expanded to a larger radius than P _o , and the formula! for the center of the mass of the annular sector P1 is provided. The shift, δ, of the annular centroid’s center of mass is shown.

FIGURE 17 shows how a spacecraft frame that can be made with multiple pairs of disc members powered by motors using solar panels.

FIGURE 18 shows the configuration of a spacecraft as per FIGURE 17 that can be made to fly in any direction in space and rapidly change direction by orientation of the activated segments of a multi-disc member configuration.

FIGURE 19 shows an airplane using the apparatus as a propelling engine.

FIGURE 20 shows a model of the apparatus as a tidal system such as an Earth-Moon system.

FIGURE 21 shows an example of how a satellite can be deviated from a circular large radius of orbit to a smaller radius of orbit and made to accelerate in orbit by a gravitational field imparted by the attraction of the Moon.

FIGURE 22 shows the configuration of a magnetohydrodynamic drive system for the apparatus without the need for a motor. The fluid rotates by means of magnetohydrodynamic propulsion when a current flows to electrodes of Opposing polarity and a magnetic-field acts to propel the fluid in a rotating flow around the disc member. When the current encounters an angular segment with opposed polarity, the fluid is repelled and the heavy ions are displaced radially to cause a centripetal change in directed forces. FIGURE 23 shows the typical parts that are required for the magnetohydrodynamic propulsion system.

FIGURE 24 shows the distribution of the electric field charges around the magnetohydrodynamic version of the apparatus.

FIGURE 25 shows the assemble magnetohydrodynamic propulsion drive with cut away views to show the relationship between the fluid components, the magnetic field and the electric field conductors.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

As required, detailed embodiments of the present invention are disclosed herein; however, it is to be understood that the disclosed embodiments are merely exemplary of the invention which may be embodied in various forms. Therefore, specific structural and functional details disclosed herein are not to be interpreted as limiting, but merely as a basis for the claims and as a representative basis for teaching one skilled in the art to variously employ the present invention in virtually any appropriately detailed structure.

Reference is now made to the drawings, wherein like characteristics and features of the present invention shown in the various FIGURES are designated by the same reference numerals.

Referring to FIGURES 1-25, for the purposes of explanation only, the following definitions apply.

1. The apparatus 10 is oriented in a frame member of reference O, with three perpendicular axes, x, y. z, defining a Space S, [x, y, z] . The x, and z, axes are taken as horizontal on the [x, z] plane, relative to the apparatus, and the y-axis is taken as vertical.

2. A shaft member 103's axis is centered to rotates about the [x,z] , and is preferably symmetrical in its span, on both sides of an encoded motor 140 it is attached to.

3. In Space S, these axes are treated as non-oriented with respect to the words vertical, and horizontal.

4. The vertical plane of symmetry refers to the [y, z] and the [x, y] planes of rotation of the disc members 200 centered on the disc member 200*s plane of rotation.

5. The horizontal plane of symmetry, refers to the horizontal plane [x,z] that passes though the axis of rotation of a shaft member 103. 6. The word vertical has no meaning in Space S, without a gravitational field, G, and as such is only used for descriptive reference, O, that the orientation of vertical along the y-axis,

7. Poling field, shall mean, the electromagnetic field Vp, that is applied to a shape- shifting material 100, during manufacture to generate an offset of its electromagnetic structure generating a directed electromagnetic field, E, in the shape-shifting material 100.

8. Shape-shifting material 100 shall mean any material such as a piezoelectric material, and a ferromagnetic fluid material that can be poled with an electromagnetic field and by either a magnetic field or an electric field, with at least the following properties: a) The shape-shifting material 100 is a radially uniform material when rotating as intended. b) The electromagnetic field, E, can cause the shape-shifting material 100 to contract or expand from a radial location of rotational symmetry. c) The shape-shifting material 100 can be held within the disc member 200.

With the above arrangement, define three perpendicular axes in a frame member of reference, O, of the apparatus 13. d) The shape-shifting material 100 can be either a piezoelectric crystal for electric field activation, or a ferromagnetic fluid for magnetic field actuation.

With the above arrangement, define three perpendicular axes in a frame member of reference, O, of the apparatus 13,

The axis, x.y.z., defining a Space S, [x,y,z], as shown in FIGURE 13 and 14. The shaft member 103, axially locates on the x-axis, to rotate symmetrically on the [x,y] plane. Each shaft member 103, holds 2 parallel disc members 200, symmetrically placed on opposite sides of an encoded motor 140, to rotate with the shaft member 103’s axial center. Each disc member 200 has shape-shifting material 100 that can be activated on shape shifting arc segments 106. Each shaft member holds two discs. Each disc member is dynamically and statically balanced around the shaft member 103,

To prevent rotations about the z-axis, two disc-members are placed to rotate on the same shaft member 103, at distal parallel [y,z] planes perpendicular to the xz -plane.

The disc members 200 are symmetrically positioned at equal distances, ±X, about the origin, x = 0,z = 0, where, , in parallel planes, [+X, y] and [-X,y _r ]. Thus, the shaft members 103 can be placed in various locations that form a symmetric pattern about the origin depending on their x,z, coordinates. The distance +X, from the origin of the disc members is determined by the array of shaft members 103 used for a given apparatus 10. The shaft members 103 can be made to form a parallel set of two shaft members 103, a triangulation of three shaft members 103 about x = 0,z = 0, a quadrature of four shaft members 103 about the point x = 0, z = 0, and many other possible geometric shapes about the origin.

The distance X, is not of consequence other than to make sure there is no interference between the shaft members 103 and the disc members 200. The number of shaft members 103 is determined by the configuration selected for the apparatus 10, and the required motions it is desired to execute. The distance X, can be adjusted to allow for the desired dynamic response of the apparatus 10 when used to propel a vehicle C.

The disc members 200 with the shape-shifting material 100, can freely rotate in the planes [+Jf,y] and [— A'.y], perpendicular to the [x, z] rotations of the shaft members 103. Advantageously, the array of shape-shifting arc segments 106 forms a symmetric and statically and dynamically balanced radial array in the origin of the [xyz] Space S. Advantageously, the array of activation arc segment 106, form a symmetric circular array in in the axis of rotation of any disc member 200.

In versions when a fluid material is used, the disc member comprises a disc member cavity disc 200b that can be sealed with a disc member cover 200a to form a uniform disc member 200 containing the shape-shifting material 100.

An apparatus 10, comprising a pair of rotating disc members 200 holding a shape-shifting material 100 with special characteristics for changing shape when an electromagnetic field is applied to angular arc segments θ°, comprising a portion of its mass distribution during fast rotation, is revealed. The apparatus 10 functions as a propulsion system for a vehicle C, in Space S, and can also function as a propulsion system for a vehicle C, in a gravitational field, G. The apparatus 10 requires energy from an encoded motor 140. If an electric motor is used, then the motor is powered by an external power source 150, such as a battery pack, a fuel, a solar panel, and other forms of mechanical energy sources. The shaft member can be powered by a convention electric motor, and a conventional motor that uses hydrocarbon fuels.

Paired sets of rapidly rotating symmetrical, statically and dynamically balanced disc members 200 are rotated by an encoded motor 140’s shaft member 103. The disc members 200 have shape-shifting material 100 with shape-shifting properties and be induced by electromagnetic fields, E, to preferably change the mass symmetry of the disc members 200, to generate directional moments and cause propulsion in a given direction. Bach paired set of disc members 200 is symmetrically positioned in the frame member of reference O, of the apparatus, to rotate in parallel planes that are perpendicular to their shaft member 103’s axis. The frame member of reference, O, may be either in Space S, or in a gravitational field, G.

Preferably, each pair of disc members 200 is symmetrically placed relative to an encoded motor 140. The disc members 200 contains a shape-shifting material 100 that can be made into a multiplicity of shape-shifting arc segments 106, that can be also be infinitely finely graded as a fluid, such as when the disc member contains a shape-shifting material 100 such a ferromagnetic fluid and a piezoelectric material. The disc member can be divided into shape- shifting arc segments 106 each subtending a small radial arc, . Therefore, each disc member 200 must have shape-shifting material 100 that can be finely angularly gradated into electromagnetical ly actuated shape-shifting arc segments 106, In general, the finer the gradation of the shape-shifting arc segments 106 that can be made, the better the apparatus 10 works for its intended purposes. The aim is to generate an angularly directed impulse that can be repeated at a particular angle selected for the direction of propulsion of the apparatus 10. As such if the disc member 200 holds a ferromagnetic material, the materials should be finely and evenly granulated for a well-defined uniform mass distribution prior to activation of shape- shifting arc segments 106.

The shape-shifting material 100 of each disc member 200 are actuated at a particular angular orientation, θ°, forming a shape-shifting arc segments 106 to change shape radially or circumferentially in that angular location only, in the frame member of reference, O. During the formation of a disc member 200, the shape-shifting arc segments 106 can be made as separated segments of the shape-shifting material 100 to prevents one shape-shifting arc segments 106 from affecting the other when an electromagnetic field E, is applied to one shape- shifting arc segments 106. If the disc member contains a shape-shifting material 100 such as a magnetic fluid, for example, a ferromagnetic fluid, then the graduations of the shape-shifting arc segments 106 can be infinite in number. The shape-shifting arc segments 106, form a part of the annular disc member 200, with shape-shifting arc segments inner radius contact face 101, of radius, R ₁ , and with shape-shifting arc segments outer radius contact face 102, of radius, The inner radius, R ₁ , can vary from the shaft radius to zero, when no shaft member 300 passes through the shape-shifting material 100. Graduations of the array of shape-shifting arc segments 106 are required if an electrical stimulus is used to prevent one shape-shifting arc segments 106 from affecting another segment, This will be the case when piezoelectric materials are used for the individual array of shape-shifting arc segments 106, Advantageously, the array of shape-shifting arc segments 106 forms a symmetric and statically and dynamically balanced array in the frame member of reference, O. The pair of electromagnetically reactive disc members 200 can be made from a disc member that encloses the array of shape-shifting arc segments 106, when each is made to function as poled shape- shifting materials 100, with radial-poled directions with respect to their axis of rotation. The disc members 200 are attached to the shaft member 103 to rotate with the shaft member 103 in a plane perpendicular to the axis of rotation, The disc members 200 when formed with the shape-shifting material 100 are in a rotationally, a dynamically, and a statically balanced state with the shaft member 103 and the encoded motor 140. As such when the shape-shifting arc material 100 is a ferromagnetic material such as a ferrofluid made from black iron oxides, F _c 3O4, held in suspension in a fluid such as kerosene, the disc members 200 has an infinite number of a continuous array of shape-shifting arc segments 106. Suitable materials for the shape-shifting material 100 include ferromagnetic fluids such as black iron oxide, with chemical structure, Fe3O4, piezoelectric materials such as ceramic piezoelectric materials and from Ceram Tec, from PZT material and from Noliac, PMN-PT materials. These shape-shifting materials 100 can be contained in disc member 200. At present, there are five types of shape- shifting materials 100 (materials that respond to pressure and tension caused by electromagnetic fields): electromagnetic fluids, ferrofluids, magnetic solid suspensions, and piezoelectric materials made from ceramic composites, polymers, and single crystals materials. Shape-shifting single crystals piezoelectric materials have generally stronger shape-shifting properties and can easily be made to fit this application. Other types of shape-shifting materials can be composed using composite metals such as Nitinol composites that can react to electromagnetic currents when cooled and heated.

Single piezoelectric material crystals such as lead-titanate [PbTiO3], and PNN, kad- nickel-niobate, [Pb(Nil/3Nb2/3)O3] are widely used materials in shape-shifting materials 100 manufacturing for specific encoded motor purposes. PVDF (poly vinylidene difluoride) is a semi -crystalline polymer with a high-energy density and contains about 48% crystals embedded in a polymeric matrix. They are easy to shape, and resilient. They are suitable for surfaces such as discs and spheres. Their shape-shifting in these materials is the result of orientation polarization of molecular dipoles. These polymers include polyimide and polyvinylidene chloride (FVDC).

External magnetic fields generated by magnets, M, can be applied to control the flow of ferrofluids and their fluid motion within the disc member 200. Ferrofluids can conveniently act as the shape-shifting material 100 of the invention. The ferromagnetic fluid can move as single component fluid acting within disc member 200.

The disc members 200 are preferably annular discs with shape-shifting arc segments 106 that have radial outer boundary surfaces equally distributed in a symmetric array around the center of rotation.

In the case, for example, of electrically reactive shape-shifting material 100, the disc members 200 can be made directly by using a suitable shape-shifting material 100 such as ceramic piezoelectric materials and from standard actuators from Ceram Tec, from PZT material and from Noliac, PMN-PT materials.

Preferably the disc member 200 is made from a suitable light material such as aluminum and other polymetric materials. The disc member 200 cab be embedded or filled with shape- shifting materia] 100 to form small independent shape-shifting arc segments 106 with a high- energy density that contain about 10% - 90% shape-shifting materials 100.

During the formation of a disc member 200, the shape-shifting arc segments 106 if made from a material that is electrically activated, can also be separated from one another by a very thin-walled boundary gap material 110, (a few hundred micrometers). The boundary gap material 110 can electrically and magnetically non-conductive elastomeric materials such as a strong flexible and non-conductive silicones, and other types of epoxies. The boundary gap material 110 prevents one shape-shifting arc segments 106 from affecting the other when an electric field, E, is applied to one and not the other. The shape-shifting arc segments 106 form an annular disc shape with a shape-shifting arc segments 106 Inner radius contact face, 101, of radius, R ₁ , and with shape-shifting arc segments 106 outer radius contact face 102, of radius, R ₂ .

The shape-shifting arc segments 106 can have an inner radius contact faces 101, that can connect electromagnetically and conductively to a concentric and cylindrical electromagnetically conductive ring which acts as a common activation contact ring 105 for electrical potential φ _E , inputs. The common activation contact ring 105 can be attached to the shape-shifting arc segment inner radius contact face 101 using either metallized coatings or an electromagnetically conductive glue, such as a silver paste soldering. Silver pastes need very low heat to fuse the common activation contact ring 105 to the shape-shifting arc segments 106. There are Kynar™ materials and other conductive tapes that may be used to attach the common activation contact ring 105 and the arc segment activation inner radius contact faces 101, respectively. Companies like Dycotec Materials, offer a range of nano, and micron flake, conductive silver pastes, that can be used. Conductive cement pastes, with conductive particles of copper, steel, and other materials may also be used as a glue. Lead-free solder and such as Superior No.30 Halide flux, commonly used in the industry can also be used to ccnduclively attach the common activation contact ring 105, and the activation arc segment 106, respectively, to the shape-shifting arc segments 106.

The shape-shifting arc segments 106 can also be made from multiple units of shape- shifting actuators that are placed in concentric radii and stacked to form separate circumferential shape-shifting are segments 106 of the disc member 200 as shown in FIGURE 10. Piezoelectric ciystal actuators are generally stacked together to form long stroke actuators. This allows one to change the extension of any shape-shifting arc segment 106 by simply actuating the selected shape-shifting arc segments 106 to extend, or to contract them either radially as previously described, or circumferentially as desired as shown in FIGURE 10. The radial mass density of the any selected shape-shifting arc segments 106 can be altered and controlled by extending or contracting that particular shape-shifting arc segments 106.

For the electrically activated version, the common activation contact ring 105 is non- conductively coupled to the shaft member 103 with an insulating cylindrical sleeve 104, to prevent any electric fields, E, upplied to the common activation contact ring 105, from contacting the shaft member 103. The insulating cylindrical sleeve 104, mechanically rotates with the common activation contact ring 105 and so does the entire disc member 200 it is attached to. The shaft member 103 can be made from a suitable material, such as, a plastic, and a metal such as for example, aluminum, and stainless steel.

Advantageously, a combination of both electric and magnetic field actuation can be achieved with this arrangement by adding a magnet M, as shown in FIGURE 8.

Polymer-based piezoelectric based shape-shifting material 100, provide large forces (few and can be made as thick polymeric shape-shifting films, forming the shape-shifting arc segment 106.

As shown in the various FIGURE 1 to 6, a shape-shifting material 100 comprises a rotating ferromagnetic fluid that i$ made up of fine granules of magnetic particles 100a suspended in a fluid. The magnetic field E _M , attracts the magnetic particles 100a along a segment of the cord CS within the disc member 200 to impede the outward radial flow of the magnetic particles 100a forming the shape-shifting material 100 contained in the disc member 200. This causes a shape-shifting to occur in a particular angular segment θ°. of rotation at radii R ₂ ~ δ, that are less than the original rotation radius R ₂ , of the path taken by the magnetic particles 100a. There is a sudden change in linear tangential momentum change, ΔM = δm(V ₂ — V1), of the moved rotating mass δm, directed to the radial angular orientation of the small arc segment θ°, of the moved mass, δm,

The centripetal forces, F _θ,R2 -δ , are lowered from the original centripetal force F _θ,R2 by the lesser radius of the flow along the segment of the cord CS, and the deceleration of the magnetic particles 100a in the segment of the cord CS will transfer the momentum of the magnetic fluid particles 100a thus diverted to the magnetic field E _M , at the radial dispositions R ₂ — δ, of the segment of the cord CS.

A motor 140 supplies rotational energy to the magnetic particles 100a in the first place. This motor 140's energy of the rotation is transferred to a sudden linear motion of the magnetic particles 100a, along the magnetic field E _M on the segment of the cord CS and causes the magnetic panicles 100a to flow along the segment of the cord CS along which the magnetic field E _M is applied. Note that the magnetic field E _M force is attractive to the magnetic materials 100a, and this attractive energy is additive to the motor 140’srotational energy acting on the magnetic particles 100a encountering the magnetic field E _M . The rotational motion now becomes a linear motion on the segment of the cord CS along the magnetic field E _M .

For convenience if the magnet M is placed on a segment of the cord CS defining a small angular orientation θ°, of the disc member 200, the shape-shifting material 100 will be attracted to the segment of the cord CS away from the larger rotation radius R ₁ . 0n the region of the applied magnetic field E _M , the magnetic particles 100a are imparting a decreasing centripetal force , on the shape-shifting arc segment 106, along the angular orientation θ° of the segment of the cord CS, until the magnetic articles 100a reach the center of the segment of the cord CS perpendicular to the radial direction, and continue to do so, but with an increasing centripetal force along the radial direction, again, until they reach the end of the segment of the cord CS and maximize the force again, F _θ,R2 , Thus, the motor 140 continuously transfers a sudden change in linear tangential momentum ΔM = δm(V ₂ — V ₁ ), of the moved rotating mass δm, causes an acceleration force directed to the radial angular orientation of the small arc segment θ°, of the moved mass, 6m,

The barycenter of the motion tends to change with the radial distribution of the mass. There is a reactive moment acting on the barycenter that tries to counter the generated momentum δm(V ₂ — V ₁ ) on the cord segment. However, using two discs counters the rotational vectors of the apparatus 10, as stated earlier. Thus, only the linear momentum, δm(V ₂ — V ₁ ), remains on the apparatus 10*

Essentially, one can think of the process as a thruster (change in pressure) of magnetic particles 100a held along the magnetic field E _M in the direction parallel to the segment of the cord CS.

Appropriate circuits 300 can be constructed to simply control the operations of apparatus 10 and provide both rotational speed control the activating electric field E’s intensity, and, the activating magnetic field E _M 's intensity that are needed to control the shape-shifting arc segment 100 as desired. The apparatus 10 may further comprise an encoded motor controller

301 to control the rotational speed cu, of the encoded motor 140, and to generate the exact oscillatory motion of the shape-shifting arc segment 100 that is needed. A propulsion circuit

302 may also be provided to control the rotational speed ω, of the encoded motor 140, of each pair of disc members 200 to offset any forces that may be required to create a difference in torques that can be used to drive the vehicle C, in different orientations of the Space S, [x, y, z].

In a gravitational field, a vehicle C, can be provided with wheels 400 that are attached to the shaft member 103 as shown in FIGURES 13, 14, and 15. Advantageously, the apparatus 10 can be used as a propulsion means in a 3-D space such as on land, in the air, Space, and in the Ocean.

A shape-shifting arc segment 106 acts as an actuator that converts an electromagnetic field, to precisely controlled radial displacements (5), of the shape-shifting arc segment 106.

Compounds made from Poly (L-lactic acid) PLLA, Poly (vinylidene fluoride-co- trifluoroethyiene) PVDF-TrFE, and Poly (vinylidene fluoride) PVDF, can be used to make the shape-shifting arc segments 106 for disc member 200, The disc member frame member 201 can be made from a strong and light-weight material such as aluminum, and from light-weight polymeric material such as PVC, polycarbonate, Kevlar, and other robust materials.

Advantageously, the shape-shifting arc segments 106 can also be made with the compounds doped with magnetic materials and also magnetically poled materials to provide for a magnetically actuated behavior.

The angular grid of isolated shape-shifting arc segments 106 can also be easily made by forming the arc segments out of any desired shape-shifting material 100 in the disc member 200. The shape-shifting arc segments 106 if solid, can be cut to shape using micro-dicing saws typically used for slicing silicon wafers and then glued to a disc frame member to between boundary gap 110s to form the disc member 200, Micro slicing can be used to precisely cut fragile materials into the shape shifting arc segments 106 without fracturing their edges. For example, both ceramic based and sintered iron magnetic shape-shifting arc segments 106 can be made the same way.

As shown in FIGURES 8, 9 and 10, the shape-shifting arc segments 106 outer radius contact faces 102 are respectively each connected to individual electrically conductive shape- shifting arc segments 106. The shape-shifting arc segments 106 are electromagnetically isolated from each other as much as possible. The shape-shifting arc segments 106 are made from electromagnetically conductive material.

Advantageously, the disc member 200 when formed, is a uniform annular and circular disc made with a symmetric array of shape-shifting arc segments 106, A common activation contact ring 105 may be used for electrical activation of the shape-shifting arc segments 106. and each shape-shifting arc segments 106 has an arc segment activation face 106 for individual activation.

Preferably, the disc member 200, when formed, has a thickness that can be chosen to determine the mass, M, of the disc member 200- The disc member 200 can also be considered as a cylinder. Other dimensional configurations may be selected without changing the basic aims of the invention. There are other ways to make the disc member 200.

For example, a shape-shifting material 100 may be used to form a disc member 200 in one piece, and still have independent shape-shifting arc segments 106 also formed in it. As mentioned before, this can be done by using various sintered ceramic-based and polymer-based shape-shifting materials of different properties and press-forming the disc member 200 as one piece with shape-shifting arc segments 106 separated by non-conductive material zones. Combinations of molded polycrystalline piezoelectric materials, doped magnetic polymers, and sintered and doped piezoelectric ceramics may also be used to achieve the same. There are other ways to form the shape-shifting arc segments 106 in a disc member 200. For example, they can be 3-D printed into the desired shape and constitution with the insulating separations, using multi -core printing technics. Vapor deposition can also be used to form the shape-shifting arc segments 106. As another example, they can be made as a multiply-stacked and electromagnetically connected shape-shifting material 100 sections that all act to provide for a larger stroke, 6, when actuated by an electromagnetic field.

The disc members 200 can also be formed by thermal spraying thermoplastic components with various concentrations of shape-shifting materials into the desired shapes that form separated shape-shifting arc segments 106, In other words, if piezoelectric materials are used, the shape-shifting arc segments 106 can be made in conventional ways of stacking them to conform to the shape-shifting arc segments 106 shapes.

Further, materials such as lithium salts and magnetic elements such as Gadolinium (Gd), and Dysprosium (Dy), Terbium (Tb), Nickel (Ni), and Cobalt (Co), can be made into fine granules that can be suspended in a fluid to form the shape-shifting material 100.

Finally, the entire disc member 200 can also be made from a single shape-shifting material without separations into individual shape-shifting arc segments 106, As said before, a ferromagnetic fluid can be used as the shape-shifting material 100, In solid form, the disc member 200 can be made by a sintering process and then “poled” with magnetic and electric particles to cause a multitude of radially directed shape-shifting arc segments 106. This can be done by electrically and alternatively, magnetically stressing the materials in defined radial directions only, in very much the same way that a multipole magnetic disc is magnetized by induction to generate bounded magnetic fields and in the same manner that a multipole piezoelectric crystal is made.

Preferably, the disc member 200 has shape-shifting arc segments 106 that are poled in a symmetric array of radial directions to form a uniform array to generate maximum stroke, 6, of the material in the poled directions only. The radial poling can be performed on shape- shifting arc segments 106 in a uniform ceramic disc member 200, for example. If made as a single unit, the material forming the shape-shifting arc segments 106 of the disc member 200 is first heated to the Curie point to allow the molecules to move freely, A strong poling electromagnetic field, V _p , is then applied in a multitude of radial directions radiating from a central hub to the perimeter for each span of a desired shape-shifting arc segments 106, to force all of the dipoles in the shape-shifting arc segments 106’s material to line up in an array of finely graded section forming a radially “poled crystal”. When the poling electromagnetic field is removed, the dipoles of the material are locked in the radial array configuration and become permanently polarized in the radial directions for either electric activation, or magnetic activation.

It is important to note that if a ferromagnetic fluid material is used for the shape-shifting arc segments 106, then, the activation arc segment 106 can be made to absorb and transmit magnetic fields instead of electric fields. The entire invention is to build an apparatus 10 that shape-shifts with electric and magnetic fields. The objective can be achieved using shape- shifting materials 100 as defined earlier, that respond to any electromagnetic fields and either to contract radially, or to expand radially in selected shape-shifting arc segments 106. The shape-shifting arc segments 106 can be made in several stacked annular arc layers that radially increase in radial arc to form a multi-stacked arc segment actuator in the radial directions, when actuated by electromagnetic fields. I have described the use of ceramic materials and polymers to create such shape-shifting arc segments 106. In the case of magnetic shape-shifting arc segments 106, one can use a stack of thin magnetically charged material layers that repel each other and when a magnetic field is imparted on a shape-shifting arc segments 106, it will radially contract or expand depending on the magnetic field E _m strength of the applied magnetic field magnetic field E _m and the magnetic field strength used to polarize the shape-shifting arc segments 106.

Thus, each disc member 200 may be also constructed as a stack of a multiplicity of small shape-shifting arc segments 106, comprising an individual shape-shifting arc segments 106 that can be activated individually and respectively, with an electric potential φ _E , or, a magnetic potential φ _M , depending on its make-up. This is done when there is a field energy difference applied between the common activation contact ring 105, and any desired number of activation arc segment 106, respectively.

Each disc member 200 has a multiplicity of shape-shifting arc segments 106, to form a dynamically and statically balanced radial array around the shaft member 103. As stated earlier, several shaft members 103 can be arrayed symmetrically to form a multi-disc member apparatus IQ. They should be arrayed to create a net zero reactive force on their barycenter of mass.

Preferably, the activated shape-shifting arc segments 106 portions of a multi-disc member 200 configuration all point in the same direction. The differences in the actuation energy and centripetal forces in two rotation of n-paired disc members 200 will generate opposite and equal reactive forces of rotation, that cancels each other and make the apparatus 10 exert a net propulsive force, 2nF, of motion in a preferred angular direction of the shape-shifting arc segment 106 as they are actuated by an electromagnetic field.

Rapid changes in electromagnetic energy applied to the shape-shifting arc segments 106 in a preferred angular radial direction θ°, of the rotating disc member 200 results in small radial changes in their shapes in the preferred angular direction θ°, changing their symmetry and their static and their dynamic balance in that direction only. Thus, the greater the number of pairs of disc members 200 used, the greater the directional force, 2nF, they generate. It is important to note that the angular orientation direction θ°, of each activated shape-shifting arc segment 100 of each disc member 200 can be oriented in a desired direction that imparts a desired overall motion to the apparatus 10. For example, all the activated shape-shifting arc segments 106 may be oriented vertically to force the vehicle C, into a horizontal motion only. Other directional vector orientations for the shape-shifting arc segments 106 may be chosen for the desired steering of a vehicle C, comprising the apparatus 10.

While the rotation of the disc members 200 is sustained by a powered motor source of energy, such as an electric motor, a gas combustion motor, a thermal engine, and other forms of motorized engines, with fuel sources such as gas, oil, diesel, solar panels, batteries and generators, all disc members 200 became asymmetrically unbalanced radially, in only preferred angular orientations of the applied fields during rotation, and they generate either a preferred shape-shifting arc segments 106 in those angular orientations only to generate a net motion in some direction. The disc members 200 "shape-shift” to generate a net propulsive force.

It is important to note that the shape-shifting of the shape-shifting arc segments 106 is not a rotating component just as the sea tide is not a rotating component in the Tide model mentioned above. It is a topological shift from symmetry, of the shape-shifting arc segments 106 in a preferred direction of Space S. The shape-shift is time Independent during rotations relative to the fixed angular disposition of the applied actuating field as it acts on the preferred shape-shifting arc segments 106. The topological shape-shift of the shape-shifting arc segments 106 of the disc member 200 does not rotate but only causes a shift of the shape-shifting arc segments 106 in a radial direction, 8°, for the activated shape-shifting arc segments 106. For example, if the topological shape shift were to rotate, it will generate an imbalance that will be transmitted to the shaft member 103 as an unbalanced system. Similarly, a Tide remains stationary as the Earth rotates.

The disc members 200 and its shape-shifting material 100, must be symmetrically, statically, and dynamically balanced prior to application of the applied electromagnetic field. The disc members 200 can have any symmetrical, statically and dynamically balanced shape, whatsoever, without the applied field. Preferably, the disc member 200’s shape-shifting arc segments 106 form circular and annular discs of a given thickness and are mounted to the shaft member 103 at axially opposite and symmetric locations.

The changes in centripetal forces in the direction of the applied electromagnetic fields to shape-shifting arc segments 106 as it arrives at the radial direction, 8°, cause changes in the shapes of the mass distribution of the shape-shifting arc segments 106 carried by disc members 200, and this results in a reactive directed change of centripetal forces and tangential momentum in those portions. The un-activated shape-shifting arc segments 106 remain circular and unchanged. Hence, changes in the static and dynamic balance occur only in the radial directions of the activated shape-shifting arc segments 106 and the symmetry of the disc member 200 in all other parts of its rotational elements is maintained.

The changes in symmetry of the disc members 200 cause an offset in centripetal force differences F _θ,R2 -F _θ,R2-δ , between the actuated shape-shifting arc segment 106 at radius R2 ± δ, and the unactuated shape-shifting material 100 of the disc members 200 at radius R, respectively. The momentum of the disc members 200 is unbalanced in the radial direction of the applied electromagnetic field, E, on the shape-shifting arc segments 106 at all times. This transfers energy from the encoded motor 140 to the shape-shifting arc segments 106 in addition to the applied electromagnetic field E’s energy, Since the disc members 200’s weight distribution outside of the actuation zone does not change, the un-activated portions of the shape-shifting material 100 of the disc members 200 remain dynamically balanced as rotating elements. However, a real force, F, arises in each disc member 200, that has a directional quality that is not rotational in nature. This force F, does not make the disc members 200 go into a state of dynamic imbalance. It is a directional force acting in the radial direction θ°, of the shape-shifting are Segments 106. As shown in FIGURE 5 and FIGURE 6, this force is transferred from the motor to the fluid and then to the frame 117 (F → 117 ).

As shown in FIGURE 16, if a portion P1 of the mass a disc member 200 is actuated by the applied electromagnetic field, E, and most of the portion Po is the unaffected portion, unchanged by the applied electromagnetic field, then, due to the equal momentum principle, the angular speed, ω , of the unaffected portion, Po, will be always be the same as the angular speed ω , of the actuated portion P|. The affected portion P1 will move at tangential velocity, ss. (R ₂ ± δ)ω , and the unaffected Po will move at a different tangential velocity Vo=(R ₂ )ω, resulting in a net centrifugal-force-difference F, in the tangential direction cf θ°.

In all embodiments of foe invention, foe apparatus 10 consists of a frame member 117, a disc member 200 and a source of fuel for the motor such as a battery 150. In the versions requiring active rotations due to a motor, (a semi-rigid disc member 200), the frame 117 holds an encoded motor 140. Advantageously, foe encoded motor 140 can also have a shaft that serves as the shaft member 103 without the need for extra bearings 105. Advantageously, the frame member 117 can also serve as a vehicle C. When assembled, the frame member 117 will hold the encoded motors 140, and any bearings 205 that hold the shaft members 103, and thus the disc members 200, to rotate about the shaft member 103’s central axis of symmetry).

In the case when a magnetohydrodynamic fluid is used, the driving rotational flow force is a magnetohydrodynamic force generated on the fluid itself without the need for a motor.

For example, the shape-shifting material 100 can be made from multiple ceramic piezoelectric crystals electrically connected in parallel to provide for an accumulated displacement that can be very large. Piezo Electric Fuel Injectors (PZO), are commonly used in gas and diesel engine engines to rapidly open and close fuel injectors using a pulsed electric potential φ _E . For example, a 35mm stacked height of piezoelectric crystal discs (diameter determines the total force) can produce a stroke, 6, of about 43 microns. This small stroke 6, is enough to make them act as electronic fuel injector actuators. Therefore, a larger stack of about 500 units with a stroke of 100 μm can provide a stroke of δ = 5cm. The example is only to show that the stroke, δ, can be increased significantly with advances in the technology,

As shown in FIGURE 8, the apparatus 10 can be made with conductive polarizing sleeve SI, attached to the frame member 117 for slidingly, and conductively contacting and transmitting either an electric potential of a given polarity or a magnetic field of a given polarity to a common activation pole ring 105 that rotates with the disc member 200. polarizing sleeve S 1 should transmit either electric energy or magnetic energy to the activate the shape-shifting arc segments 106. polarizing sleeve S1 can be a magnet for example that has an angular attraction for the materials forming shape-shifting arc segments 106, polarizing sleeve SI can also be an electric pole for biasing the electrical polarity of the shape-shifting arc segments 106,

The apparatus 10 further consists of one or more polarizing segments S2, attached to the frame member 117 to selectively activate shape-shifting arc segments 106 in some angular span, say, θ°, where the angle, θ°, is measured from the vertical y-axis of symmetry and centered through the x-axis of the rotation. Polarizing segments S2 should transmit electric energy and magnetic energy to the activate the shape-shifting arc segments 106. Polarizing segments S2 can be magnet materials that can transmit an electromagnetic field to the shape- shifting arc segments 106. Polarizing segments S2 can also be an electrically conductive material for biasing the electrical polarity of the shape-shifting arc segments 106 in one angular direction for the shape-shifting arc segments 106 that are selected for activation. For the electric field, a pole of the electric field E+ is connected by a lead wire 151 to one polarity of the power source 150’s output terminal, and the polarizing segments S2 is also connected by a lead wire 152 to the opposite polarity of the power source 150’s output terminal.

As shown in FIGURES 9, 10 and 11, advantageously, the shape-shifting arc segments 106 can also be actuated by circumferential actuators 109 made ftom piezoelectric crystals or magnetically active materials that change shape. The circumferential actuator 109 separate massive shape-shifting arc segments 106 that form a radially symmetric circumferential array around shaft member 103. The circumferential actuator 109 are positioned in small radial gaps 108 between the shape-shifting arc segments 106. The shape-shifting arc segments 106 can be made from metals of high density, and when actuated by the circumferential actuator 109, they move circumferentially changing the radial mass distribution as shown. The shape-shifting arc segments 106, the circumferential actuator 109, and the shaft member 103 and motor 140 are dynamically and statically balanced. The circumferential array of shape-shifting arc segments 106 are separated by small radial gaps 108. The shape-shifting arc segments 106 are placed between circumferential actuator 109 in the circumferential array. When actuated, a shape- shifting arc segment 106 will be displaced circumferentially to change the radial mass distribution of the disc member 200. The maximum radial gaps 108 determines the extent to which any two massive shape-shifting arc segments 106 can be displaced in relation to one another In this configuration, the shape-shifting arc segments 106 must be supported on the shaft member 103 to flex by means of a thin spring portion 100s that holds them steady on shaft member 103,

As shown in FIGURE 10, multiple shape-shifting arc segments 106 and multiple circumferential actuators 109 are used to change the distribution of massive shape-shifting arc segments 106 on disc member 200.

The circumferential mass distribution of the disc member 200 can be changed by increasing or decreasing the circumferential distribution of the shape-shifting arc segments 106 of the disc member 200, when a particular arc segment θ° is extended, or contracted, by the circumferential actuators 109 at the same fixed angular orientation of the apparatus 10. Extending and contracting circumferential actuators 109 causes the angular distribution and the radial distribution of matter in the shape-shifting arc segments 106 of the disc member 200 to change, resulting in the desired changes in centrifugal forces F, generated on the disc member 200 at a particular arc segment θ°. In essence, the circumferential array of the shape- shifting arc segments 106 and circumferential actuators 109 makes disc member 200 performs the same function as that of radial change in the shape-shifting arc segments 106, by redistribution of mass of the shape-shifting material 100 in the activated set of shape-shifting arc segments 106.

It is further advantageous that each of the radial array of circumferential actuators 109 can be made from a stack of either circumferential or radial actuators to generate larger strokes.

The array of circumferential actuators 109 activates the shape-shifting arc segments 106, to either expand and increase their angular disposition 6, in relation to the frame member 117, thus either increasing or contracting the angular distribution 0 and the radial distribution R2,Rz ± δ, of matter distribution of the disc member 200, in order to change the radial distribution of the shape-shifting material 100. The change in the circumferential and angular change of the shape-shifting material 100 will result in a redistribution of radial mass of the shape-shifting material 100 in disc member 200.

This solid form of the apparatus 10 has the advantage of simplicity, The shape-shifting material 100 can be made as equally massive members separated by small equal radial gaps 108 and forming a continuous symmetrical circumferentially and radial array. The radial gaps 108 can be separated changed by either piezoelectric discs or piezoelectric cylinders that act as small circumferential actuators 109 that expand and contract. Thus, by activating the circumferential actuators 109 between the shape-shifting arc segments 106 of one sector S1S2 of the disc member 200 can be either contracted or expanded while the other sector S2S 1 can be either left un-activated or conversely, can be either expanded, and contracted as shown in FIGURE 10 and 11.

The material of the circumferential actuators 109 can be selected to either be magnetically active, or electrically active, and a combination of both. As said before, electric actuation can be achieved with piezoelectric crystals. Magnetic actuation can easily be achieved by simply placing a magnet in the path of the circumferential actuators 109 to transmit a magnetic field that can pull the shape-shifting arc segments 106 and cause them for example to contract circumferentially. material 100 could simply be massive magnets 100, acted upon by a strong external magnet M, attached to a fixed point of the frame 117. The external magnetic M is positioned at a fixed angular orientation of the frame 117 with its magnetic pole (for example the south pole S), opposing the magnetic poles (south pole, S) of the shape-shifting material 100 in each shape-shifting arc segment 106. When the shape- shifting material 100 is in the arc segment θ°, the shape-shifting material 100, in this case a magnet; is pushed away from the maximum radius R ₂ , of its original centrifuged location, to a smaller radius of rotation R ₂ — δ,. This causes an imbalance of centrifugal forces F around the disc member 200, resulting in a smaller centrifugal force F _θ , acting in the shape-shifted arc segment θ°,

In all the particular means and ways, the apparatus 10 can be built, it is important that the forces that generate the change in the mass distribution be greater than the centrifugal forces that are generated in each shape-shifting arc segment 106 by the rotation. For example, the piezoelectric actuators E, should be able to either pull the shape-shifting material 100 into either larger orbits, or smaller orbits when actuated. Similarly, the magnetic field actuator M, should be able to either pull the shape-shifting material 100 into either larger orbits, or smaller orbits when actuated. If these actuating forces are capable of lifting the entire apparatus 10 by their actions, then a repetitive actuation of these forces can impulsively lift the entire apparatus 10 against gravity. In space for example. The apparatus will exert a force that should be able to either pull the shape-shifting material 100 into either larger orbits, or smaller orbits when actuated. Similarly, in the ocean, a submarine’s weight that is countered by its buoyancy, will not impede the forces generated. In as much as a simple magnet can generate forces capable of lifting a motor, the disc member and its contents, and a frame, it becomes obvious that the apparatus 10 has a tremendous potential for propulsion of flying cars, and airplanes. For example, a magnetic of length 13.5 in, width 7.5 in, and height I0.2in weighs approximately 97 lbs, but has a rated lift force load of lOOOlbs,

Considering FIGURE 13, suppose four-disc member 200 are placed on the axles of vehicle C, Each disc member 200 has a total distribution of shape-shifting arc segments 106 in an angular span of 2π -radians (around the circle). Let the axis of rotation of each shaft members 103 of four-disc members 200 be in the x-direction, and let the rotational plane of the disc member 200 be the [x, y]-planes forming a planar array.

Let the total mass of a disc members 200 be equal to T (kg).

Let the actuated shape-shifting arc segments 106 span angular an angle, θ°, subtended symmetrically about the horizontal x-axis of the rotations, in each of the disc members 200*s rotational plane in the upper [y,x] planes.

Considering FIGURES 12 and 13, let the outer radius, R ₂ , of the shape-shifting arc segments 106 be extended to a new radial distribution, (R2 + δ), in the activated angular span, θ°. Here, δ, is cither positive, or, negative quantity. For explanation purposes, let δ be a positive displacement. Then, neglecting the gaps between them, rhe mass, M, of the extended T segment of shape-shifting arc segments 106 of the disc member 200, is equal to M = — 9. Therefore, only the mass distribution of shape-shifting arc segments 106 of the angular span, θ° is changed by the applied potential to either extend, or, contract, symmetrically about the z- axis, in the [y,z] plane.

As shown in FIGURE 11, the shape-shifting arc segments 106 that are present in the arc segment, in the will extend symmetrically and dynamically , and change the shape of the disc member 200 from a perfect circle to a symmetric bulge or (depression) about the y-axis spanning θ°, in the [y, z] plane of the disc member 200, This bulge is made in a preferred direction, θ°. This slight change in mass distribution of the shape-shifting arc segments 106 in disc member 200 in the arc segment, θ°, will cause an imbalance of centripetal forces, F, on each of the disc members 200, in the directional span of This angular imbalance in density distribution results in a change in centripetal forces and results In a tangential force F, acting in the y, direction on all the disc members 200. These forces are shown in FIGURE 13 in the upper plane [x,y] plane. This force F, tends to generate a counter moment to rotate the barycenter of the vehicle C about shaft member 103 of the apparatus 10 in lower [x,y] plane of the apparatus 10. Since these reactive forces to the forces F, are opposed to each other in the frame 117, there will be no net rotation of the vehicle C about a shaft member 103. However, as explained earlier, the forces F, become impulsive acceleration forces in the upper [y, z]- plane.

To counter the reaction of the forces F, and nullify any rotation, the apparatus 10 must have at least two-disc members 200, symmetrically placed on the x-axis as stated above, to generate equal and opposite forces that balance with equal and opposite momenta to stop the rotation of the apparatus 10, in the x-directions.

One Can imagine that the centripetal forces will tend act in the y-direction, and will tend to rotate the shaft member 103, and encoded motor 140 in the [x,y] plane since they create a moment about the axis of rotation of the apparatus 10. When two-disc members 200 are used, and they are symmetrically placed equidistant on the x-axis of rotation, this gives a total force of 2.F, in the same y-direction, and this removes the imbalance. Thus, the rotations caused by the forces, F, can be converted to a net vertical force, 2F in the vertical y-direction, only.

It is preferable that the encoded motor shaft member 103 extends equally in two directions, along the axis of rotational symmetry to allow two-disc members 200 to be positioned on opposite sides of the encoded motor 140 to counterbalance each other, As shown in FIGURE 22, 23, 24, and 25, a shape-shifting material 100 comprises a rotating magnetohydrodynamic fluid such as an electrolyte solution with heavy metallic cations C ⁺ . The solution of the shape-shifting material 100 that is made up of heavy metallic cations C ⁺ that respond to magnetic field E _M in a magnetohydrodynamic flow (MHD-flow) of ions suspended in a fluid motion RF . The magnetic field E _M , imposes a motive force to rotate the magnetohydrodynamic fluid without the need for a motor. Circumferential actuator 109a, and 109b, 109c act as electrodes placed peripheral to a large radius (R ₂ + d) to move the fluid in a substantially circular rotary motion around an annular chamber 113 frame and housing member 117. The heavy metallic cations C ⁺ and the light anions A" are released into the flow by oppositely charged circumferential electric actuators 109a, and 109b, 109c, respectively. Between electric actuator 109a and electric actuator 109b, the heavy metallic cations C ⁺ are attracted and confined to the negatively charged circumferential actuators 109a, the heavy metal cations C ⁺ flow along peripheral paths close to the larger radius of the negatively charged circumferential actuator 109a, while the negatively charged anions A" are attracted to the positive charge along the smaller radius of the circumferential actuator 109b. Both circumferential actuator 109a and circumferential actuator 109b are restricted to a fixed angle (360 - θ) ^o , such that they do not encompass the actuation segment θ° along the path of flow. The metallic cations C ⁺ that pass from the region of influence of circumferential actuator 109a and circumferential actuator 109b now enter into the electric influence of circumferential actuator 109c in a restricted angle of actuation segment θ°, where the heavy metallic cations C ^T encounter an electric repulsive force E, due to the like positive charge of the circumferential actuator 109c. This repulsive force of circumferential actuator 109c pushes the metallic cations C ⁺ to a smaller radius (R ₂ ), and generating a centripetal force difference F, along the actuation segment θ°. This difference causes a propulsive force F that is transmitted to the apparatus frame 117 to cause propulsion.

Upon exiting the segment θ°, the cations again flow to the larger radius, (R ₂ + δ), to repeat the process of propulsion continuously. When the metallic cations C ⁺ encounter the circumferential actuator 109c, they are repelled toward the smaller radial path R ₂ flow without resistance along the depression 115, This causes a shape-shifting to occur in a particular angular segment θ°, of rotation at radii R ₂ , that is less than the original rotation radius R ₂ + δ. There is a sudden change in linear tangential momentum change, ΔM = δm(V ₂ — V ₁ ), of the moved rotating metallic cations C ⁺ of mass δm, that is directed perpendicular to the radial angular orientation of the small arc segment of θ°.

The centripetal forces, F _θ,R2 , are lowered from the original centripetal force by the lesser radius of the flow along the segment of the cord of the arc segment θ°. A power source 150 such as a battery charged by solar power or electric sources supplies the magnetohydrodynamic energy E to the metallic cations C ⁴ . This loss of centripetal momentum is transferred to a sudden linear impulse motion in the direction of the arc segment θ°. It is convenient to place the magnetics M over the fluid flow between the circumferential actuators 109a and 109b to maximize the magnetohydrodynamic forces. Any electrolyte such as ferrous based electrolytes may be used.

It is convenient to use electrolytes with metallic anions and anions such as Electrolytes with of alkaloids, oxides, carbon compounds, sulfur compounds, Zintl anion-compounds of the valence form, [M = M] ^n- with the anion valence electron configuration [(n + 1)s ² (n + l)p)n-, [V(CO)6]-, [Nb(CO)6]-, [Ta(C0)6]-, [Mn(CO) ₅ ]-,[Mn(CO) ₆ ]-, [Ir(CO)4]- ,[Co(CO)»], that have negative metal anions. These electrolytes can be made to form the anions in solution by half-cathodic reactions, without releasing a gas or deteriorating the electrolyte solution. For example, a 9 ⁺ oxidation state has been found for IrO4.

The apparatus 10 comprises a fixed frame 117 supporting a magnetohydrodynamic fluid which is ashape shifting material 100, contained in a sealed annular space, S. The sealed annular space S comprises an inner boundary wall 114 parallel to the contour of an outer boundary wall 116; said inner boundary wall 114 and said outer boundary wall 116 being respectively, and sealingly connected perpendicularly to a top wall 112 and to a bottom wall 1 1, to form said scaled annular space S; at least one of said top wall 112 and said bottom wall 111 comprising a non-conductive and magnetically permeable material; a magnetic field MF generating means directing a magnetic field MF perpendicular to, and passing through at least one of said top wall 112 and said bottom wall 111, into said sealed annular space S. A portion of the inner wall 114 comprises an electrically conductive first electrode circumferential actuator 109b subtending a circular arc segment of fixed angle θ°, less than 360° relative to said fixed frame 117. A portion of said outer wall 116 comprising an outer wall second electrode circumferential actuator 109a subtending a circular arc segment of the said fixed angle θ° relative to said fixed frame; a portion of said outer wall 116 comprising a third electrode circumferential actuator 109c subtending a circular arc segment not included in said fixed angle θ° relative to said fixed frame 117. A portion of said inner wall 1 14 having a radially symmetric depression oriented radially inwardly and said depression 113 subtending a circular arc segment of the not including said fixed angle θ° relative to said fixed frame 117. The first electrode circumferential actuator 109b and said third electrode circumferential actuator 109c are electrically coupled with electrical conductor 151 from an electrical power source 150 to conduct the same voltage polarity such that when a voltage potential of opposite polarity is applied to the first electrode circumferential actuator 109b with conductor 152, a magnetohydrodynainic flow fluid motion R _F is generated in said magnetohydrodynamic fluid to flow rapidly between said first electrode circumferential actuator 109b and second electrode circumferential actuator 109a through said fixed angle θ° relative to said fixed frame 117 in the sealed annular space S; and cations C ⁴ " are generated along the surfaces of the negatively charged said second electrode circumferential actuator 109a along said outer wall 116, and anions A" are generated along the inner wall 114 and such that when the cations C* flowing along the said outer wall 116 encounter said third electrode circumferential actuator 109c, they are repelled by the positive charge of the third electrode circumferential actuator 109c to flow along the depression 115 of the inner wall 114 to a smaller radial location R ₂ Jess than the radius R ₂ + δ of the outer wall 116. Then, the change in mass distribution of the heavy cations C ⁺ generates a difference in centripetal forces F, in the direction of said fixed angle θ° causing a motive force F on the apparatus 10.

The polarity of the first electrode circumferential actuator 109 b, said second electrode circumferential actuator 109a and the third electrode circumferential actuator 109c can be reversed to rotate the fluid in the opposite direction to achieve the same result. The top wall 112 and bottom wall 11 1 are made from non-conductive magnetically permeable materials. The first electrode circumferential actuator 109c, the second electrode circumferential actuator 109a and the third electrode circumferential actuator 109c are made from a corruption-resistant and conductive materials such as stainless steel and conductive ceramics.

If the rotation is uniform of angular speed, to, then, the reactive difference in centripetal force, 2F generated by the actuated shape-shifting arc segments 106, in the upper [y,z] planes, depends on its angular extent, θ and the stroke, δ'.

Let the mass, T, of the uniform disc be evenly distributed on the disc member 200 and let the shape-shifting arc segments 106 have an inner radius R1 and outer radius R ₂ . The mass, M, of the activated shape-shifting material 100 is given by:

The centroid, r, of an arc segment of angular extent, 6, of inner radius 1^ and outer radius R ₂ is given by:

The shift in centroids is given by:

Let the force generated by the centripetal force difference be F _C1 and let the reactive force imposed on the shaft member 103 by given by FR, and let the force of activation due to the electromagnetic field be F _E . The differences in centripetal forces, F, due to the encoded motor 140 acting on the centroids of arc segments, θ°, of shape-shifting material 100 of mass, M, that arrive at any given time period in the arc segments, θ° in the upper [y,z] plane, and the uniform unexpanded arc segments of the same arc measure is given by the differences in the shift of the centroid, <5, for the centripetal forces acting on the centroid for each disc member:

Since the encoded motor 140 can have energy that is greater than the activation reactive forces, and the force applies to both shaft members 103 and the shape-shifting arc segments 106, we can assume the activation reactive forces to be small compared to the centripetal forces, F.

The relation can be reduced to simple form as follows, There, are two scenarios: a) The apparatus 10 as described is stable in the rotations that can be caused by the equal forces, 2F on the two-disc members 200. However, it is still unstable, and has a rotational force component about the axis of rotation of the shaft member 103, by the action and reaction principle. When the apparatus 10 is used with a vehicle C, in a gravitational field, this problem by be alleviated by using gravity to stabilize the vehicle C. To alleviate this problem, suppose the apparatus 10 is used to power a vehicle C, of mass, W Kg. IP is the total weight of the apparatus 10 and the vehicle C, Then, in a gravitational field, the apparatus 10 can be stabilized by gravitational fields, if the center of mass of the vehicle C, is below the forces, 2F, In other words, the weight W will stabilize the vehicle C, b) If the apparatus 10 is to lift the vehicle C, against gravity, then, the force, 2F, must be greater than some minimum value, equal to the net gravitational force, Wg, acting on the total vehicle C's weight, W, where g is the gravitational acceleration at the location of the vehicle C. A vehicle C, can be constructed that will have a net center of gravity below the forces, 2F, keeping the vehicle C is a steady orientation, (swinging below the lifting force, 2F). Obviously, the sway of the vehicle C, will be in the [y,z] -directions, and so the vehicle C’s center of gravity can be made to off-set the tendency of the vehicle C, to sway. Then, for lift off against gravity to happen, the force F, in the vertical direction, y, must balance the gravitational force on the total vehicle C’s weight W, plus the weight of the disc member, and so must satisfy the centroid relation for the forces acting on the annular segment of the centroid:

Where, g is the gravitational acceleration of the earth (9.81ms ^-2 ), or in the case of a foreign planet that the vehicle C is in, the planet’s g.

The gravitational field, G, and the net upward forces, will keep the vehicle C, from sway as they act on the vehicle C, to keep it moving in the direction of the lifting force, 2F. Think of this as lifting a mass tied to a string on a pivot above the mass. However, the sway is not eliminated by this arrangement of two disc members 200. The problem can also be eliminated by the following setup of the apparatus 10.

This relationship can be reduced to the general form:

It is clear that the relationship will yield positive values for W> 0, if;

TABLE 3 below shows a series of solutions for the net weight, IT kg that can be lifted against gravity by the apparatus 10 with one disc member 200, if the parameters are chosen as show in the TABLE 2.

It is clear that there are solutions for ω , that will cause lift-off for the parameters chosen in TABLE 2. The actual weight of a craft, C of total weight, W kg, that can be lifted, including passemgers and power sources, for the prameters in TABLE 2 are a function of the angular speed, ω.

TABLE 3 below shows the amount of weight, W, in Kg that can be lifted at a particular angular speed by a disc member that is specified in TABLE 2 above. In free Space S, the relationship of the planes [x,y][y,z][x, z] are relative to the apparatus 10, shaft member 103, and have no bearing to the concept of vertical. As such one must define “vertical” as the y-axis, relative to an observer’s frame member of reference, O, as shown in FIGURE 13. The tendency of the vehicle C, to rotate about the shaft member 103, can be eliminated by simply doubling the components of the apparatus 10, and providing for two parallel shaft members 103, two encoded motors 140, and four parallel disc member 200 held in platform, P as shown in FIGURE 13.

In this case, the arrangement is doubled, with 4 parallel rotating disc members 200. Two of the disc members 200 are coupled to the same shaft member 103 as described earlier. Two other disc members 200 are coupled to another shaft member 103 to rotate in an opposite direction to counterbalance the shafts members I OS’s rotations.

The platform P, acts as the relative horizontal frame member of reference of the observer,

O. Then, there will be 4-directional force vectors 4F, on the platform acting in the same y- direction in a balanced mode as shown in FIGURE 8. In this case, as in the above case, the vehicle C, can be steered by slightly changing the rotational speed of each of the paired disc members 200. The solutions for various subtended angles of for the activated shape-shifting arc segments 106 in TABLE 2, clearly show that the apparatus 10 can lift a vehicle C, with a weight W kg, against gravity. More so, the apparatus 10 will work more efficiently in a gravity - free Space S,

The phenomenon of magnetic particles moving in a rotating frame leads to additional advantages of the apparatus 10. In experiments, it was observed that when power is cut off from the motor, the change in centripetal forces generated by the magnetic field acting on the magnetic particles MF, and 100a, as shown in FIGURES 5, 6, and 22, results in stored energy in the apparatus 10. This is due to the returning of the energy of the braking force of the magnetic field MF.

While the invention has been described, disclosed, illustrated and shown in various terms or certain embodiments or modifications which it has assumed in practice, the scope of the invention is not intended to be, nor should it be deemed to be, limited thereby and such other modifications or embodiments as may be suggested by the teachings herein are particularly reserved especially as they fail within the breadth and scope of the claims here appended.