An Extended Variational Formulation for Isothermal Gas-Dynamic Lubrication

Abstract

An extended variational formulation is derived which can be applied to problems in isothermal compressible flow where the medium obeys the perfect gas law. The Reynold’s approximations for fluid film lubrication have been applied to this variational formulation to obtain an expression that is applicable to the field of gas-dynamic lubrication. This variational formulation for gas-dynamic lubrication has as its Euler-Lagrange equation, the Reynolds’ equation of lubrication for a perfect gas. The extended variational formulation is shown to differ from the classical Lagrangian expression with respect to its form and to its applicability to nonlinear problems.