Multibody Dynamics in Natural Coordinates through Automatic Differentiation and High-Index DAE Solving

The Natural Coordinates (NCs) method for Lagrangian modelling and simulation of multibody systems is valued for giving simple, sparse models. We describe our version of it and compare with the classical approach of Jalan and Bayo (JBNCs). Our NCs use the high-index differential-algebraic equation solver DAETS. Algorithmic differentiation, not symbolic algebra, forms the equations of motion from the Lagrangian. We obtain significantly smaller equation systems than JBNCs, at the cost of a non-constant mass matrix for fully 3D models a minor downside in the DAETS context. Examples in 2D and 3D are presented, with numerical results.