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.
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On the Variational Principle and Lagrange Equations in Studies of Gasdynamic Lubrication
L. N. Tao
Illinois Institute of Technology, Chicago, Ill.
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Tao, L. N. (March 1, 1964). "On the Variational Principle and Lagrange Equations in Studies of Gasdynamic Lubrication." ASME. J. Appl. Mech. March 1964; 31(1): 43–46. https://doi.org/10.1115/1.3629568
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