Solution of the Hamilton-Jacobi equation for certain dissipative classical mechanical systems

Abstract

Recent developments have shown that the pure Lagrange‐Hamiltonian formalisms can be extended to problems (chiefly, classical systems involving dissipative forces) previously regarded as outside such theories. The Hamilton‐Jacobi equations corresponding to certain such systems are given here, and the structure, separability, and solution of these equations are studied. Examples treated here include a particle moving freely and under a constant force in a viscous medium, the damped‐harmonic oscillator in one and three dimensions, and a particle moving in one dimension with quadratic friction in an arbitrary potential. In all cases, the Hamilton‐Jacobi equation separates into time and space components, and the complete solution is obtained.