Multibody System Analysis Based on Hamilton's Weak Principle

Abstract

The double pendulum, a simple system that exhibits complex dynamics, is used to demonstrate a method based on Hamilton’ s weak principle (HWP) for assembling and solving the maximum coordinate set equations for a multibody system. Results calculated using HWP are compared to a reference solution obtained by integrating the ordinary differential equations (ODE) in minimum coordinate set form. The HWP solution is shown to be comparable to the ODE solution in accuracy and computational efe ciency. These results suggest an alternative architecture for multibody system analysis, which implements the maximum coordinate set form of the system equations, and a simple, efe cient, and robust solution algorithm.