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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > The Lie algebra of classical mechanics

## The Lie algebra of classical mechanicsAdd to your list(s) Download to your calendar using vCal - Robert McLachlan (Massey University)
- Wednesday 07 August 2019, 15:00-16:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact INI IT. GCS - Geometry, compatibility and structure preservation in computational differential equations Classical mechanical systems are defined by their kinetic and potential energies. They generate a Lie algebra under the canonical Poisson bracket which is useful in geometric integration. But because the kinetic energy is quadratic in the momenta, the Lie algebra obeys identities beyond those implied by skew symmetry and the Jacobi identity. Some Poisson brackets, or combinations of brackets, are zero for all choices of kinetic and potential energy. Therefore, we study and give a complete description of the universal object in this setting, the ‘Lie algebra of classical mechanics’ modelled on the Lie algebra generated by kinetic and potential energy of a simple mechanical system with respect to the canonical Poisson bracket. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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