Breakdown of the connection between symmetries and conservation laws for semiholonomic systems

TL;DR

This paper demonstrates that the established link between symmetries and conservation laws in holonomic systems does not necessarily apply to semiholonomic systems, challenging a common assumption in Lagrangian mechanics.

Contribution

It provides a specific example and analysis showing the breakdown of the symmetry-conservation law connection in semiholonomic systems.

Findings

Symmetries do not always imply conservation laws in semiholonomic systems.

Holonomic and semiholonomic constraints are not equivalent in their relation to symmetries.

The traditional link between symmetries and conservation laws is limited to holonomic systems.

Abstract

Integrable velocity-dependent constraints are said to be semiholonomic. For good reasons, holonomic and semiholonomic constraints are thought to be indistinguishable in Lagrangian mechanics. This well-founded belief notwithstanding, here we show by means of an example and a broad analysis that the connection between symmetries and conservation laws, which holds for holonomic systems, is not valid in general for systems subject to semiholonomic constraints.