Geometric Mechanics, Variational Integrators, and Asteroid Pairs

Jerrold Marsden, Control and Dynamical systems, California Institute of Technology

Geometric mechanics deals with mechanical systems with symmetry with an infusion of ideas from geometry, analysis and dynamical systems. A few highlights from its successes over the years will be reviewed. One of its more interesting interactions has been the development of discrete mechanics and corresponding integration algorithms, with applications to long term integrations of, for instance, point vortices as well as to dynamical problems in elasticity. An excellent recent example of the use of geometric mechanics is to an analysis of the dynamics and dissociation rates of asteroid and Kuiper belt pairs.