Hamiltonian-Jacobi Treatment of Damped Harmonic Oscillator Based on Employing the Method of Dual Coordinates

Abstract

Hamiltonian-Jacobi Treatment of Damped Harmonic Oscillator Based on Employing the Method of Dual Coordinates
Mohammad A. Al-Btoush*
Amal F. Al-Maaitah
Khaled I. Nawafleh
Abstract
In this paper, we provide the canonical approach for studying the damped harmonic oscillator based on the doubling of degrees of freedom approach. Explicit expressions for Lagrangians of the elementary modes of the problem and characterising both forward and backward time propagations are given. A Hamiltonian analysis showing the equivalence with the Lagrangian approach is also done. To this end, the techniques of separation of variables were applied.
Keywords: Doubling of degrees of freedom; Dissipated harmonic oscillator; Hamilton-Jacobi; Time-independent Lagrangians.