Investigation of the Benefits and Effectiveness of Hamilton's Weak Principle for Multibody Sytems Analysis

Abstract

This paper demonstrates that a Hamilton’s Weak Principle (HWP) based direct solution applied to simple multibody problem, the planar double pendulum, rivals the accuracy of conventional multibody analysis formulations, yet is easily derived using a maximum coordinate set. The HWP direct solution is derived from a low-order nite element discretization of the Hamilton’s Law of Varying Action (HLVA), casting the problem as nding the roots of a non-linear system. The system is formulated in maximum coordinates by applying the constraints to HLVA with the method of Lagrange multipliers. The direct solution circumvents the need to derive or integrate the di erential (algabraic) Euler-Lagrange equations of motion. The e ectiveness, convergence and relative simplicity of the direct solution relative to the conventional models is demonstrated.