Publication 25-CNA-022

Hamilton-Jacobi as Model Reduction, Extension to Newtonian Particle Mechanics, and a Wave Mechanical Curiosity

Amit Acharya
Dept. of Civil & Environmental Engineering
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
acharyaamit@cmu.edu

Abstract: The Hamilton-Jacobi equation of classical mechanics is approached as a model reduction of conservative particle mechanics where the velocity degrees-of-freedom are eliminated. This viewpoint allows an extension of the associations of the Hamilton-Jacobi equation from conservative systems to general Newtonian particle systems involving non-conservative forces, including dissipative ones. A geometric optics approximation leads to a dissipative Schrödinger equation, with the expected limiting form when the associated classical force system involves conservative forces.

Get the paper in its entirety as  25-CNA-022.pdf

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