Reduction of invariant constrained systems using anholonomic frames

TL;DR

This paper explores two methods for reducing invariant nonholonomic systems using anholonomic frames, providing a geometric approach to simplify the equations of motion in systems with symmetry.

Contribution

It introduces a unified geometric framework for reducing invariant nonholonomic systems via anholonomic frames, enhancing understanding of their dynamics.

Findings

Reduced equations expressed in anholonomic frames

Unified geometric approach to reduction methods

Simplified analysis of invariant nonholonomic systems

Abstract

We analyze two reduction methods for nonholonomic systems that are invariant under the action of a Lie group on the configuration space. Our approach for obtaining the reduced equations is entirely based on the observation that the dynamics can be represented by a second-order differential equations vector field and that in both cases the reduced dynamics can be described by expressing that vector field in terms of an appropriately chosen anholonomic frame.