Journal of Applied Mathematics
Volume 2005 (2005), Issue 4, Pages 365-382

Dynamic model of multi-rigid-body systems based on particle dynamics with recursive approach

Hazem Ali Attia1,2

1Department of Engineering Mathematics and Physics, Faculty of Engineering, El-Fayoum University, El-Fayoum, Egypt
2Department of Mathematics, College of Science, A-Qasseem University, P.O. Box 237, Buraidah 81999, Saudi Arabia

Received 28 September 2004; Revised 17 August 2005

Copyright © 2005 Hazem Ali Attia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A dynamic model for multi-rigid-body systems which consists of interconnected rigid bodies based on particle dynamics and a recursive approach is presented. The method uses the concepts of linear and angular momentums to generate the rigid body equations of motion in terms of the Cartesian coordinates of a dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotational transformation matrix. For the open-chain system, the equations of motion are generated recursively along the serial chains. A closed-chain system is transformed to open-chain by cutting suitable kinematical joints and introducing cut-joint constraints. An example is chosen to demonstrate the generality and simplicity of the developed formulation.