Numerical Modeling Methods for Large Open Loop Multibody System

Abstract

A pendulum’s motion was stated to be as a way to illustrate the movement of human body in the studies of multibody system. Therefore, a comparison between the two numerical models in multibody systems were implemented on the articulated pendulums of different sizes. The two numerical models were known as the augmented Lagrangian formulation and fully recursive method. In order to identify the difference performance of the numerical models, various size of articulated pendulums has been tested which are 2, 4, 8, 16, 20 and 40 pendulums. Differential equations developed from both models were solved by using Runge-Kutta 4 and 5. Both models were coded in Matlab and have been optimized in order to ensure only related routine were considered. The performance was evaluated based on the computing time with constant relative and absolute tolerance in Runge-Kutta solver which is 0.01 s. All pendulums were assumed to have the same weight, angle and length. As for the results, the augmented Lagrangian formulation solved the differential equations faster than the fully recursive method when tested up to 20 pendulums. However, fully recursive method started to solve the differential equations faster than the augmented Lagrangian method when it need to deal with a very large system such as 40 pendulums and above. Thus, it can be concluded that the suitable method to solve the small, open loop system such as articulated pendulums is augmented Lagrangian method while for a very large system, the fully recursive method will be more efficient.