Download PDFOpen PDF in browserHalf-Explicit Runge-Kutta Lie Group Integrators for Flexible Multibody SystemsEasyChair Preprint 134072 pages•Date: May 22, 2024AbstractWhen modelling geometrically exact beams under constraints, two problems arise:The presence of nonlinear configuration spaces for describing large rotations and the presence of algebraic variables coupled with differential ones. To obtain an efficient numerical solution for the latter problem, half-explicit Runge-Kutta methods have been introduced in 1992 by Brasey and Hairer. The current work adapts these half-explicit Runge-Kutta methods to solve DAEs in nonlinear configuration spaces, of the Lie group form, so that the first problem is covered. The study aims at the analysis of the so called drift-off effect, which is a deviation from the constraints at position level when evaluating the numerical solution of the index-2 DAEs. Specifically, we adapt classical techniques for avoiding the drift-off effect to nonlinear configuration spaces. To conclude the study, numerical experiments on flexible structures modelled as Cosserat rods are performed. Keyphrases: Drift-off effect, Half-explicit Runge-Kutta, Index-2 Baumgarte formulation, Lie groups time integration
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