Hamilton’s principle and approximate solutions to problems in classical mechanics

Abstract

Ordinarily in classical mechanics Hamilton’s principle is used as a variational method to obtain the Euler–Lagrange equations of motion. In general these differential equations can be solved only by approximation methods. The Ritz method is a procedure for obtaining approximate solutions of problems expressed in variational form directly from the variational equation. Application of this method to problems in classical mechanics is discussed, and the example of a simple pendulum is examined in detail. The result is a perturbation series type of solution. Secular terms in the solution are avoided in a natural way.