Geometric properties of projective constraint violation stabilization method for generally constrained multibody systems on manifolds |
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Authors: | Zdravko Terze Joris Naudet |
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Affiliation: | (1) Department of Aeronautical Engineering, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia;(2) Department of Mechanical Engineering, Multibody Mechanics Group, Vrije Universiteit Brussel, Brussels, Belgium |
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Abstract: | During numerical forward dynamics of constrained multibody systems, a numerical violation of system kinematical constraints
is the important issue that has to be properly treated. In this paper, the stabilized time-integration procedure, whose constraint
stabilization step is based on the projection of integration results to underlying constraint manifold via post-integration
correction of the selected coordinates is discussed. A selection of the coordinates is based on the optimization algorithm
for coordinates partitioning. After discussing geometric background of the optimization algorithm, new formulae for optimized
partitioning of the generalized coordinates are derived. Beside in the framework of the proposed stabilization algorithm,
the new formulae can be used for other integration applications where coordinates partitioning is needed. Holonomic and non-holonomic
systems are analyzed and optimal partitioning at the position and velocity level are considered further. By comparing the
proposed stabilization method to other projective algorithms reported in the literature, the geometric and stabilization issues
of the method are addressed. A numerical example that illustrates application of the method to constraint violation stabilization
of non-holonomic multibody system is reported.
An erratum to this article can be found at |
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Keywords: | Constraint violation stabilization Optimized partitioning of generalized coordinates Projective stabilization methods Manifolds |
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