Dynamic analysis of multi-body systems using tangent coordinates

This paper presents an efficient method for the dynamic analysis of multi-body systems subjected to constraints. The solution of the dynamic system lies on a manifold of lower dimensions. This information is used to develop the equations of motion in tangent space. Using this approach, only the minimum number of coordinates defining the response of the system are required to be integrated. This leads to a reduction in the computer time and memory requirements. The system equations of motion are integrated using the predictor-corrector method. The invariance property of the distance between two points is used to check if the tangent space needs to be redefined. Two numerical examples, one that has a fixed number of constraints and another that has a variable kinematic topology, are presented to demonstrate the versatility and efficiency of the present method.