Transition to the case of "resolved gauge" in the Lagrange-Poincaré equations for a mechanical system with symmetry on the total space of a principal fiber bundle whose base is the bundle space of the associated bundle

Abstract

This note is a continuation of our earlier articles arXiv:1612.08897 and arXiv:1709.09030, where using the dependent coordinates the local Lagrange-Poincaré equations were obtained for a mechanical system with symmetry describing the motion of two interacting scalar particles on a special Riemannian manifold (the product of the total space of the principal fiber bundle and vector space), on which a free proper and isometric action of a compact semisimple Lie group is given. Assuming the existence of the parametric representations for local sections in the principal bundle, we make the transition to independent coordinates in the obtained Lagrange-Poincaré equations.

11 pages

References in corpus (2)

• 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
• Coordinate representation of the Lagrange-Poincaré equations for a mechanical system with symmetry on the total space of a principal fiber bundle whose base is the bundle space of the associated bundle

Cited by in corpus (1)

• On the geometric representation of the path integral reduction Jacobian for a mechanical system with symmetry given on a manifold that is a product of the total space of the principal fiber bundle and the vector space