Parametrized formulations of Hamilton's law for numerical solutions of dynamic problems: Part I. Global approximation

Abstract

Many dynamic problems can be solved numerically by using Hamilton's law. The solution is expressed as a series in the time domain with undetermined coefficients. The unknown coefficients are determined by satisfying the Hamilton's law when the solution is allowed to have certain types of variations. The advantage of the method is that it can directly generate a set of algebraic equations without considering the dynamic equilibrium or the governing differential equations. In this paper, the essential features of the Hamilton's law and its variations are re-examined from the numerical perspectives. A general version of variation is proposed and the parametrized formulations are presented. The parametrized formulations unify conventional formulations and also yield many new ones. Illustrative numerical examples in this paper demonstrate that the conventional formulations may not be optimal although they may be rational.