Regularity and symmetries of nonholonomic systems

TL;DR

This paper explores the geometric structure, symmetries, and conserved quantities of nonholonomic Lagrangian systems using linearly singular differential equations, including examples like the relativistic particle.

Contribution

It provides a geometric framework for analyzing nonholonomic systems as linearly singular differential equations, with new insights into their symmetries and constants of motion.

Findings

Nonholonomic constraints can be incorporated into a singular differential equations framework.

The relativistic particle with nonholonomic velocity constraint forms a regular system.

Symmetries and conserved quantities are characterized within this geometric approach.

Abstract

Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are studied within the framework of linearly singular differential equations. Some examples are given; in particular the well-known singular lagrangian of the relativistic particle, which with the nonholonomic constraint v^2=c^2 yields a regular system.