A robust and efficient Lie group solver for Cosserat rod models with internal and external constraints

Abstract

This thesis explores multibody dynamics, focusing on real-time simulations of flexible slender structures like rods and cables. A novel solver is developed by adapting half-explicit Runge-Kutta (HE-RK) methods to nonlinear Lie group configuration spaces, using unit quaternions to handle large rotations without singularities. Unlike implicit schemes, this approach is non-iterative, significantly reducing computational costs while maintaining high accuracy. The solver includes variable time step control and addresses the numerical drift-off effect via adapted Baumgarte stabilization and projection techniques. Convergence and robustness are validated using benchmarks like the heavy top, the roll-up manoeuvre, and the flying spaghetti test case. Results confirm that this Lie group solver effectively balances computational efficiency with accuracy, providing a robust tool for advanced mechanical and industrial applications.