TABLE OF CONTENTS In this paper several formulations for automatic generation of the equations of motion for rigid and rigid-deformable multibody systems are reviewed. The rigid-body formulations are the body-coordinate formulation based on Newton-Euler equations, a non-conventional point-coordinate formulation where rigid bodies are represented as a collection of particles, and the joint coordinate formulation that employs relative coordinates between bodies. A transformation process based on velocity relations is described for easy transformation of one formulation into another. Finally, a brief overview of the equations of motion for deformable bodies in a multibody environment is presented.
Key words: multibody dynamics; rigid bodies; deformable bodies; body coordinates; point coordinates; joint coordinates; equations of motion.
Derivation of equations of motion for computational multibody dynamics has been the topic of many research activities. The scope of these activities has been quite broad. Some techniques allow us to generate the equations of motion in terms of a large set of differential-algebraic equations. Other techniques yield the equations of motion as a minimal set of ordinary differential equations. Many other in-between approaches provide us with various alternatives. Each formulation has its own advantages and disadvantages depending on the application and our priorities.
Possibly, the simplest method to construct the equations of motion is in the form of a large set of differential-algebraic equations. The configuration of a rigid body is described by a set of translational and rotational coordinates. Algebraic...
