Newtonian-based methodologies in multi-body dynamics

Three commonly used methods of formulating the equations of motion for multi-body systems are reviewed in this paper. Two of these methods are Newtonian-based; i.e. the entire formulations can be derived simply based on the knowledge of Newton's laws of motion. These two methodologies result in formulations that contain many algebraic and differential equations suitable for computational procedures. The number of equations in these formulations increases as the number of moving bodies and the number of kinematic joints increase. The third reviewed methodology provides a systematic process to transform the large number of equations from any of the other two formulations to a smaller set, possibly to as many as the number of degrees of freedom in the system. This process preserves the simplicity of the original Newtonian-based formulation and, at the same time, provides significant improvement in the computational efficiency and numerical stability in any dynamic analyses.