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A unified mathematical treatm ent of thick and thin film elastohydro dynamic lubrication problems is presented. The construction of approxi mate solutions is discussed by using Ritz-Galerkin methods with piecewise polynomial basis functions. In particular for the line contact problem, smooth Hermite and cubic spline spaces are used to obtain solutions over a wide load-speed range. Pressure 'spikes' are obtained. N o m e n c l a t u r e Hertzian half-width Breadth of slider modified Youngdoi:10.1098/rspa.1975.0068 fatcat:33i2mvc2irbyplah4x6kmfdibe