Conservation of energy and momenta in nonholonomic systems with affine constraints

TL;DR

This paper investigates the conditions under which energy and momentum are conserved in nonholonomic systems with affine constraints, using geometric tools like the reaction-annihilator distribution.

Contribution

It provides a geometric characterization of conservation laws in nonholonomic systems with affine constraints, extending previous results to include gauge-like generalizations.

Findings

Conservation of energy depends on the reaction-annihilator distribution.

Conditions for momentum conservation are characterized geometrically.

The framework applies to a broad class of nonholonomic systems with affine constraints.

Abstract

We characterize the conditions for the conservation of the energy and of the components of the momentum maps of lifted actions, and of their `gauge-like' generalizations, in time-independent nonholonomic mechanical systems with affine constraints. These conditions involve geometrical and mechanical properties of the system, and are codified in the so-called reaction-annihilator distribution.