Performance Analysis of VON MISES’ Motor Calculus within Modelica

Tobias Zaiczek
Fraunhofer Institute for Integrated Circuits, Design Automation Division, Dresden, Germany

Olaf Enge-Rosenblatt
Fraunhofer Institute for Integrated Circuits, Design Automation Division, Dresden, Germany

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp09430105

Ingår i: Proceedings of the 7th International Modelica Conference; Como; Italy; 20-22 September 2009

Linköping Electronic Conference Proceedings 43:30, s. 278-287

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Publicerad: 2009-12-29

ISBN: 978-91-7393-513-5

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


This paper presents an alternative concept of modelling multibody systems within Modelica; the socalled motor calculus. This approach was introduced by R. VON MISES in 1924 and can be used to describe the dynamical behaviour of spatial multibody systems in a very efficient way. While the equations clearly take a very simple form in terms of motor algebra; the numerical efficiency is still an open question.

In the paper; first some fundamentals of motor calculus are summarized. An experimental implementation of motor algebra is used to measure and analyse the numerical efficiency and performance regarding the simulation time of VON MISES’ approach. Therefore; some components of the Modelica Multibody Standard Library were modified in order to compare both implementations. Finally; some examples are given to prove the applicability and correctness of the concept but also to serve as a basis for a discussion of the numerical performance. The chosen approach utilizes all object-oriented features provided by the modelling language. Besides; it gives reason for the present endeavours to introduce the possibility of operator overloading within Modelica.


Motor calculus; screw theory; rigid multibody system; Modelica; performance


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