Non-holonomic constraints: Considerations on the least action principle also from a thermodynamic viewpoint

TL;DR

This paper addresses the challenge of applying the least action principle to non-holonomic constraints, proposing a response that aligns with physical behavior and incorporates thermodynamic principles.

Contribution

It introduces a novel approach to reconcile the least action principle with non-holonomic constraints using thermodynamic considerations.

Findings

Proposes a new method for non-holonomic systems

Aligns least action principle with thermodynamics

Improves understanding of constrained dynamics

Abstract

The principle of least action seems not to lead to equations describing the motion consistent with the physical behaviour, for non-holonomic constraints. Here, a response is proposed for this fundamental problem in Mathematical Physics. Some considerations are also developed, based on the first and second law of thermodynamics.