Multibody System Dynamics

, Volume 14, Issue 3–4, pp 301–316 | Cite as

An Integrated Runge–Kutta Root Finding Method for Reliable Collision Detection in Multibody Systems

  • Gerald GrabnerEmail author
  • Andrés Kecskeméthy


Described in this paper is an integrated approach for reliable detection of state events occurring during numerical integration of the equations of motion of multibody systems. The method combines an explicit Runge–Kutta 4/5 Dormand scheme with continuous dense output extension with a polynomial root detection algorithm warranting root detection for large time steps enclosing several roots. The method is implemented in C++ and integrated within an object-oriented code for simulation of the equations of motion of mechanical systems including collisions. Numerical comparisons with standard methods are shown for a number of test examples, displaying the robustness of the method.


events impacts integration mechanical systems polynomials 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Siemens Transportation SystemsGrazAustria
  2. 2.Chair for MechanicsUniversity Duisburg-EssenDuisburgGermany

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