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Constrained Multibody Dynamics With Python: From Symbolic Equation Generation to Publication

[+] Author Affiliations
Gilbert Gede, Dale L. Peterson, Angadh S. Nanjangud, Jason K. Moore, Mont Hubbard

University of California, Davis, CA

Paper No. DETC2013-13470, pp. V07BT10A051; 10 pages
  • ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 7B: 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Portland, Oregon, USA, August 4–7, 2013
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5597-3
  • Copyright © 2013 by ASME


Symbolic equations of motion (EOMs) for multibody systems are desirable for simulation, stability analyses, control system design, and parameter studies. Despite this, the majority of engineering software designed to analyze multibody systems are numeric in nature (or present a purely numeric user interface). To our knowledge, none of the existing software packages are 1) fully symbolic, 2) open source, and 3) implemented in a popular, general, purpose high level programming language. In response, we extended SymPy (an existing computer algebra system implemented in Python) with functionality for derivation of symbolic EOMs for constrained multibody systems with many degrees of freedom. We present the design and implementation of the software and cover the basic usage and workflow for solving and analyzing problems. The intended audience is the academic research community, graduate and advanced undergraduate students, and those in industry analyzing multibody systems. We demonstrate the software by deriving the EOMs of a N-link pendulum, show its capabilities for LATEX output, and how it integrates with other Python scientific libraries — allowing for numerical simulation, publication quality plotting, animation, and online notebooks designed for sharing results. This software fills a unique role in dynamics and is attractive to academics and industry because of its BSD open source license which permits open source or commercial use of the code.

Copyright © 2013 by ASME



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