engleski

DAE Index 1 Formulation for Multibody System Dynamics in Lie-Group Setting

A Lie-group integration method for constrained multibody systems is proposed in the paper and applied for numerical simulation of a satellite dynamics. Mathematical model of multibody system dynamics is shaped as DAE system of equations of index 1, while dynamics is evolving on Lie-group introduced as system ‘state-space formulation’. The basis of the method is Munthe-Kaas algorithm for ODE on Liegroups, which is re-formulated and expanded to be applicable for the integration of constrained multibody dynamics in DAE index 1 form. The constraint violation stabilization algorithm at the generalized position and velocity level is introduced by using two different algorithms: a first one that operates directly on the ‘state-space’ manifold and, a second one, that uses Cartesian rotation vectors as local coordinates for the generalized positions. A numerical example of ‘dual-spin’ satellite that demonstrates the proposed integration procedure is described and discussed at the end of the paper.

Lie-groups; Multibody Systems Dynamics; Numerical Integration Methods; DAE systems; Constraint Violation Stabilization; Manifolds; Munthe-Kaas method

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