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Energy-momentum conserving integration of multibody dynamics

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Abstract

A rotationless formulation of multibody dynamics is presented, which is especially beneficial to the design of energy-momentum conserving integration schemes. The proposed approach facilitates the stable numerical integration of the differential algebraic equations governing the motion of both open-loop and closed-loop multibody systems. A coordinate augmentation technique for the incorporation of rotational degrees of freedom and associated torques is newly proposed. Subsequent to the discretization, size-reductions are performed to lower the computational costs and improve the numerical conditioning. In this connection, a new approach to the systematic design of discrete null space matrices for closed-loop systems is presented. Two numerical examples are given to evaluate the numerical properties of the proposed algorithms.

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Authors and Affiliations

  1. Chair of Computational Mechanics, Department of Mechanical Engineering, University of Siegen, Siegen, Germany

    Peter Betsch & Stefan Uhlar

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  1. Peter Betsch
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  2. Stefan Uhlar
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Correspondence to Peter Betsch.

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Betsch, P., Uhlar, S. Energy-momentum conserving integration of multibody dynamics. Multibody Syst Dyn 17, 243–289 (2007). https://doi.org/10.1007/s11044-007-9043-9

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  • DOI: https://doi.org/10.1007/s11044-007-9043-9

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