On the Hamilton-Jacobi equation for second class constrained systems

TL;DR

This paper presents a general method for deriving the Hamilton-Jacobi equation in second-class constrained systems, demonstrated through examples that confirm the approach yields correct solutions to the Euler-Lagrange equations.

Contribution

It introduces a systematic procedure for obtaining the Hamilton-Jacobi equation in second-class constrained systems, validated by explicit examples.

Findings

Successfully derives Hamilton-Jacobi equations for various second-class systems

Confirms that the method produces solutions consistent with Euler-Lagrange equations

Provides explicit examples illustrating the procedure

Abstract

We discuss a general procedure for arriving at the Hamilton-Jacobi equation of second-class constrained systems, and illustrate it in terms of a number of examples by explicitely obtaining the respective Hamilton principal function, and verifying that it leads to the correct solution to the Euler-Lagrange equations.