engleski

Lie-Group Integration Method for Constrained Multibody Systems in Stabilized DAE-Index-1 Form

A coordinate free Lie-group integration method for the constrained multibody systems (MBS) is proposed in the paper. Mathematical model of MBS dynamics is shaped as DAE system of equations of index 1, while dynamics is evolving on the system state-space modeled as a Lie-group. Since formulated integration algorithm operates directly on the system manifold via MBS elements’ angular velocities and rotational matrices, no local coordinates are necessary and kinematical differential equations are completely avoided. A basis of the integration procedure is the Munthe- Kaas algorithm for ODE integration on the Lie- groups, which is re-formulated and expanded to be applicable for the integration of constrained MBS in DAE-index-1 form. In order to eliminate numerical constraint violation for the generalized positions and velocities during the integration procedure, two constraint stabilization algorithms are introduced: a projection method based on the constrained least square minimization algorithm via system global coordinates and the one-step non-iterative constraint manifold projection method by using local exponential coordinates. Two numerical examples, heavy top dynamics and satellite with mounted 5 DOF manipulator, are presented and documented. The proposed Lie-group DAE-index-1 integration method is easy-to-use for the MBS with the kinematical constraints of a general type and it is especially suitable for dynamics of the mechanical systems with a large 3D rotation motion domain.

lie-groups ; multibody systems dynamics ; numerical integration methods ; dae systems ; constraint violation stabilization ; munthe-kaas integration algorithm ; special orthogonal group so(3)

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