Nonholonomic Constraints: a New Viewpoint

TL;DR

This paper introduces a new geometric framework for nonholonomic mechanics by viewing the Euler-Lagrange equations as unconstrained on a modified algebroid structure, unifying various cases and enabling symmetry-based integrals.

Contribution

It presents a novel formalism that interprets nonholonomic Euler-Lagrange equations as unconstrained equations on a new algebroid, broadening the theoretical understanding.

Findings

Unified treatment of nonholonomic systems

Derivation of a Neoether Theorem variant

Identification of first integrals via symmetries

Abstract

The purpose of this paper is to show that, at least for Lagrangians of mechanical type, nonholonomic Euler-Lagrange equations for a nonholonomic linear constraint D may be viewed as non-constrained Euler-Lagrange equations but on a new (generally not Lie) algebroid structure on D. The proposed novel formalism allows us to treat in a unified way a variety of situations in nonholonomic mechanics and gives rise to a version of Neoether Theorem producing actual first integrals in case of symmetries.