Elastic Multibody Systems – The Subsystem Ordinary Differential Equations

Chapter 6: Boris Galerkin1 published his method in (B.G. Galerkin, 1915). For a special case, the procedure had already been anticipated by I.G. Bubnov in 1913. The method is therefore sometimes referred to as the Bubnov-Galerkin method. According to (M.S. Smirnov, 2003), Galerkin’s method “provides the approximate solution of a variational problem without minimization of an energy functional but using transformed differential equations”; its original application field is mainly characterized by his original paper entitled series solution of some problems in elastic equilibrium of rods and plates. The procedure is, however, not restricted to linear elasticity problems but obviously reveals its main power in the field of approximate solutions of nonlinear systems, thus extended by G.I. Petrov to nonlinear problems in gas dynamics, hydrodynamics and aerodynamics in 1940 (referred to then as the Galerkin-Petrov method). It is sometimes also called the Ritz-Galerkin method, based on a comparison with W. Ritz’s contribution from 1909.