Generalized Hamilton-Jacobi equations for nonholonomic dynamics

TL;DR

This paper derives generalized Hamilton-Jacobi equations for nonholonomic systems with linear velocity constraints, showing that solutions lead to minimized action, extending classical variational principles.

Contribution

It introduces a nonlinear Lagrange functional approach to formulate Hamilton-Jacobi equations for constrained dynamical systems, providing a new theoretical framework.

Findings

Existence of solutions implies action minimization.

Generalized equations extend classical Hamilton-Jacobi theory.

Applicable to systems with linear velocity constraints.

Abstract

Employing a suitable nonlinear Lagrange functional, we derive generalized Hamilton-Jacobi equations for dynamical systems subject to linear velocity constraints. As long as a solution of the generalized Hamilton-Jacobi equation exists, the action is actually minimized (not just extremized).