A Framework for Spatial 3D Collision Models: Theory and Validation

Abstract

This project puts forth a framework for spatial collision models for bodies. The framework leverages a new method in dynamics to calculate the relevant post-collision trajectory in 3D space. The new method exploits Cartan’s notion of moving frames and places frames of reference on all moving (and colliding) bodies. Next, it exploits Lie group theory SO(3) and its associated algebra, so(3), to relate such frames to each other. Finally, it exploits a compact notation to streamline the mathematics. This project presents a numerical validation of the results using MSC Adams and compares the rotation and translation values of the bodies with those found using the new method. ThreeD web pages display the results using WebGL.