Galerkin's method in mechanics and differential equations

Abstract

The method to be described here is attributed to the Russian investigator V. G. Galerkin, whose original papers are inaccessible to the present writer. His knowledge of the method is derived from a description given in a paper by E. P. Grossman. Grossman states that the method was given by Galerkin in his treatise 'Rods and Plates' (Vestnik Ingeneroff, 1915, p. 897) and that applications to oscillation problems were first made by V. P. Lyskov. It is pointed out by Grossman that Galerkin's process in applications to mechanics leads to the same results as Lagrange's principle of virtual work, but employs a special co-ordinate system.