Speaker
Description
Simulating the dynamics of multibody systems involves dealing with finite rotations, which presents a key challenge in numerical mechanics due to the fact that rotations are governed by nonlinear transformations. In this contribution, we utilize a mixed variational time approach to analyze rigid body dynamics. Time integration is based on a discretization of the Hamilton`s principle for constrained systems, using a finite element formulation in time. Consequently the equations of motion assume the form of differential-algebraic equations (DAEs). Therefore, an approximation of the Lagrange multipliers is also necessary. Moreover quaternions offer an efficient way to describe rotations, avoiding singularities encountered with other representations. This procedure provides both a systematic framework for generating time-stepping methods and a possibility of a global solution over the entire time interval. The latter can be used to solve boundary value problems that require a flow of information backwards in time. This approach may serve as a foundation for addressing more advanced problems in inverse dynamics and optimal control for rigid bodies. We apply the integration scheme to representative mechanical rigid body systems to investigate the numerical properties.
