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Symbolic linearization of equations of motion of constrained multibody systems

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Abstract

Many common dynamic mechanical systems are subject to configuration or velocity constraints. Analysis of such systems often requires linearized forms of the motion equations. To address this issue, we developed a procedure for organizing the constraint and motion equations and their subsequent linearization. This procedure was developed for equations of motion generated by Kane’s method, where dependent states have not been algebraically eliminated; it is compatible with any method as long as only ordinary differential equations are required to describe the system (i.e., no differential algebraic equations). Following a brief review of Kane’s method and the structure of the equations it generates, we present the procedure to symbolically linearize the nonlinear motion equations of constrained multibody systems, and illustrate it with an example of the rolling disk.

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Acknowledgements

This material is based upon work partially supported by the National Science Foundation under award 0928339 and three Google Summer of Code projects (2009, 2011, 2012). Jason Moore, Thomas Johnston, Evan Sperber, and Andrew Kickertz provided valuable feedback during discussions of multibody dynamics and control.

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  1. Sports Biomechanics Laboratory, Department of Mechanical and Aerospace Engineering, University of California Davis, Davis, CA, 95616-5294, USA

    Dale L. Peterson, Gilbert Gede & Mont Hubbard

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  1. Dale L. Peterson
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  2. Gilbert Gede
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  3. Mont Hubbard
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Correspondence to Dale L. Peterson.

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Peterson, D.L., Gede, G. & Hubbard, M. Symbolic linearization of equations of motion of constrained multibody systems. Multibody Syst Dyn 33, 143–161 (2015). https://doi.org/10.1007/s11044-014-9436-5

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  • DOI: https://doi.org/10.1007/s11044-014-9436-5

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