Title: Lagrangian reduction for simple mechanical systems with constant orbit type
Detail: Control and Dynamical Systems Seminar, California Institute of Technology, 1997/09/08

An action of a Lie group G on a manifold Q is said to be of constant orbit type if the isotropy group of q1Q is conjugate to the isotropy group of q2Q for each q1,q2Q. In such cases the group orbits are each diffeomorphic to a homogenous space of the group G. We thus begin by investigating simple mechanical systems (i.e., those whose Lagrangians are kinetic minus potential energies) whose configuration manifold is a homogeneous space (generalising the Euler-Poincaré equations). We then use the structure of these systems to discuss the local geometry of general simple mechanical systems with a symmetry group giving an action of constant orbit type.

No online version avaliable.

Andrew D. Lewis (andrew at mast.queensu.ca)