A Performance Comparison of Several Lie Group Integration Methods for Solving the Equations of Constrained Multibody Dynamics

EasyChair Preprint 13546

Abstract

When expressed in absolute coordinates, the constrained multibody dynamics problem results in a system of index-3 differential algebraic equations (DAEs). In previous works, we explored three Lie group integration methods for solving these DAEs: fully-implicit, half-implicit, and velocity coordinate partitioning. It was found that these methods are computationally more efficient in approximating the solution to the equations of motion than methods which rely on Euler angles or Euler parameters as generalized coordinates. In this work, we directly compare the accuracy and performance of the three Lie group approaches to solving the index-3 DAEs. The Python code developed to generate the reported results is open-source and available in a public repository for reproducibility studies.

Keyphrases: Lie group integration, Multibody dynamics, computational methods, differential-algebraic equations, numerical integration

@booklet{EasyChair:13546,
  author    = {Alexandra Kissel and Luning Bakke and Dan Negrut},
  title     = {A Performance Comparison of Several Lie Group Integration Methods for Solving the Equations of Constrained Multibody Dynamics},
  howpublished = {EasyChair Preprint 13546},
  year      = {EasyChair, 2024}}