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TECHNICAL PAPERS

Nonseparable Solutions to the Hamilton-Jacobi Equation

[+] Author and Article Information
C. M. Leech

Department of Mechanical Engineering, UMIST, Manchester M60 1QD, UK

B. Tabarrok

Department of Mechanical Engineering, University of Victoria, Victoria, Canada

J. Appl. Mech 64(3), 636-641 (Sep 01, 1997) (6 pages) doi:10.1115/1.2788940 History: Revised January 04, 1994; Received January 07, 1995; Online October 25, 2007

Abstract

The Hamilton-Jacobi partial differential equation is solved for potential energy functionals of constant, linear, and quadratic form using a class of nonseparable solutions; these solutions give a geometric property to the generating solution, embedding it into the class of conics. These solutions have two basic components, that designated as a kernel component which belongs to the system regardless of the specific dynamics of the system and the primary and secondary system functions that are dependent on the specific initial conditions. Solutions are obtained for the linear oscillator, a rheonomic oscillator and a two-degree-of-freedom system, the latter suggesting an approach for general multidegree-of-freedom systems.

Copyright © 1997 by The American Society of Mechanical Engineers
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