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

Abstract

Using the dependent coordinates, the local Lagrange-Poincaré equations and equations for the relative equilibria are obtained for a mechanical system with a 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 the vector space) on which a free proper and isometric action of a compact semi-simple Lie group is given. As in gauge theories, dependent coordinates are implicitly determined by means of equations representing the local sections of the principal fiber bundle.

additions to the article 1612:08897. arXiv admin note: text overlap with arXiv:1612.08897

References 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

Cited by in corpus (3)

• 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
• The Lagrange-Poincaré equations for interacting Yang-Mills and scalar fields
• 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