Nonholonomic constrains: why does not the least action principle leads to equations describing the motion consistent with the physical behaviour?

TL;DR

This paper investigates why the least action principle fails to produce equations of motion that match physical behavior in systems with nonholonomic constraints and proposes an explanation for this discrepancy.

Contribution

The paper offers a new understanding of the limitations of the least action principle in nonholonomic systems and provides an explanation for the inconsistency with physical motion.

Findings

Identifies the mismatch between least action principle and physical behavior in nonholonomic systems

Proposes a theoretical explanation for the failure of the least action principle in these cases

Suggests alternative approaches to modeling nonholonomic constraints

Abstract

The least action principle seems not to lead to equations describing the motion consistent with the physical behavior for nonholonomic constrains. Here an answer to this question in proposed.