Strong degenerate constraining in Lagrangian dynamics

TL;DR

This paper investigates the complex problem of strong degeneracy in Lagrangian dynamics with codimension one constraints, introducing novel analysis of degenerate potentials and revealing unexpected effects.

Contribution

It is the first to analyze degenerate potentials in the strong constraining problem for Lagrangian dynamics with codimension one.

Findings

Includes analysis of real analytic potentials previously unconsidered

Identifies counterintuitive effects of degenerate constraining

Extends understanding of degeneracy in Lagrangian systems

Abstract

We study the strong constraining problem in Lagrangian dynamics in the degenerate codimension one case. This is the first time that degenerate potentials at the constraint are considered for this problem. These new results cover several real analytic potentials that the previous do not. Some counterintuitive effects of the degenerate constraining problem are discussed.