The Hamilton-Jacobi Equation Applied to Continuum

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

Department of Mechanical Engineering, UMIST, Manchester M60 1QD, U.K.

J. Appl. Mech 64(3), 658-663 (Sep 01, 1997) (6 pages) doi:10.1115/1.2788943 History: Received June 29, 1995; Revised August 29, 1996; Online October 25, 2007


The Hamilton-Jacobi partial differential equation is established for continuum systems; to do this a new concept in material distributions is introduced. The Lagrangian and Hamiltonian are developed, so that the Hamilton-Jacobi equation can be formulated and the principal function defined. Finally the principal function is constructed for the dynamics of a one-dimensional linear elastic bar; the solution for its’ vibrations is then established following the differentiation of the principal function.

Copyright © 1997 by The American Society of Mechanical Engineers
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