Chetaev vs. vakonomic prescriptions in constrained field theories with parametrized variational calculus

TL;DR

This paper compares Chetaev and vakonomic approaches in constrained field theories, demonstrating how parametrized variational calculus derives their equations and highlighting an example where the non-holonomic method yields unphysical results.

Contribution

It introduces a framework using parametrized variational calculus to derive and compare Chetaev and vakonomic field equations, clarifying their physical relevance.

Findings

Vakonomic and Chetaev variations are characterized within the framework.

Parametrized variational calculus effectively derives their respective field equations.

An example shows the non-holonomic method can produce unphysical results.

Abstract

Starting from a characterization of admissible Cheataev and vakonomic variations in a field theory with constraints we show how the so called parametrized variational calculus can help to derive the vakonomic and the non-holonomic field equations. We present an example in field theory where the non-holonomic method proved to be unphysical.