Abstract
A method that decides the optimal stabilization constant of the constraint stabilization method is developed for both the real time constant step integration and the variable order, variable step integration methods. The stability theory for multistep integration formulas is applied to determine the stability region of the stabilized constraint equations. An algorithm that maintains error control of the constraint equations as well as the system integration variables is developed. The proposed algorithm is implemented on the variable step, variable order DE algorithm [1]. A kinetic constraint equation is formulated, based on the energy conservation theorem. Violation of the kinetic constraint equation is corrected by stabilizing the equations of motion. Application of the proposed methods to the real time simulation is discussed. Several examples are solved to demonstrate the effectiveness of the proposed methods.
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Bae, DS., Yang, SM. (1990). A Stabilization Method for Kinematic and Kinetic Constraint Equations. In: Haug, E.J., Deyo, R.C. (eds) Real-Time Integration Methods for Mechanical System Simulation. NATO ASI Series, vol 69. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76159-1_11
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DOI: https://doi.org/10.1007/978-3-642-76159-1_11
Publisher Name: Springer, Berlin, Heidelberg
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