On the Variational Principle and Lagrange Equations in Studies of Gasdynamic Lubrication

[+] Author and Article Information
L. N. Tao

Illinois Institute of Technology, Chicago, Ill.

J. Appl. Mech 31(1), 43-46 (Mar 01, 1964) (4 pages) doi:10.1115/1.3629568 History: Received March 14, 1963; Online September 15, 2011


The paper is concerned with the variational formulation in studies of gasdynamic lubrication. It is shown that Reynolds’ equation of lubrication is equivalent to a set of Lagrange equations similar to those in classical dynamics. The Lagrangian and the dissipation-production are defined. Furthermore, based on the Hamiltonian principle for the field of a continuum, the Lagrangian density and the dissipation-production density are established. This formulation includes the incompressible problem, which is obtainable from the Helmholtz-Rayleigh principle of minimum energy-dissipation, as a special case. Hence a unification of the variational methods for both gasdynamic and hydrodynamic lubrication is accomplished.

Copyright © 1964 by ASME
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