Dependent coordinates in the Lagrange-Poincaré equations for mechanical systems with symmetry

Abstract

The Lagrange--Poincaré equations for the mechanical system describing the motion of a scalar particle on a Riemannian manifold with a given free and isometric action of a compact Lie group is obtained. In an arising principle fibre bundle, the total space of which serves as a configuration space of the considered mechanical system, the local description of the reduced motion is done in terms of dependent coordinates. In obtaining of the equations we use the variational principle developed by Poincaré for the mechanical systems with a symmetry.

20 pages

Cited by in corpus (1)

• The Lagrange-Poincaré equations for a mechanical system with symmetry on the principal fiber bundle over the base represented by the bundle space of the associated bundle