Lie Groups and the Principle of Virtual Work Applied to Systems of Linked Rigid Bodies. A generic algorithm for the equations of motion using the moving frame method in engineering

Abstract

This thesis explores the possibility of a generic algorithm for systems of linked rigid bodies using the moving frame method (MFM) in engineering developed by H. Murakami and T.Impelluso. The project entails the construction of a generic algorithm for the equations of motion and the validation of the equations generated by said algorithm. The validation is done by comparing the equations of motion generated by the algorithm to equations evaluated manually. Furthermore, the resulting behavior from integration is compared to those from the Hamilton canonical equations of motion. Finally, a real-life model is built to see if the theory holds in reality. Naturally, when taking the step to bring in reality, friction and air resistance will have to be taken into account. Therefore, the equations of motion were supplemented with friction models constructed to match the movement of the real-life model.