Multibody System Dynamics

, Volume 26, Issue 1, pp 1–14 | Cite as

Smooth velocity approximation for constrained systems in real-time simulation

  • Bernhard Burgermeister
  • Martin Arnold
  • Alexander Eichberger


The rapidly increasing complexity of multi-body system models in applications like vehicle dynamics, robotics and bio-mechanics requires qualitative new solution methods to slash computing times for the dynamical simulation.

Detailed multi-body systems are designed for accurate off-line simulation. For real-time applications or efficient long-term simulations simplified models are used (Rill, G.: J. Braz. Soc. Mech. Sci. XIX(2):192–206 (1997)). In contrast to pure numerical model reduction techniques (Antoulas, A.C.: Approximation of large-scale dynamical systems (2005) and Fehr, J., Eberhard, P.: J. Comput. Nonlinear Dyn. 5:031005 (2010)), the presented quasi-static solution method is based on analytical model reduction combined with adapted numerical methods for evaluating and solving the (reduced) equations of motion efficiently and focuses on accelerated computation of the low frequency parts of the solution of the nonlinear equations of motion by smoothing out the velocities of fast moving low-mass bodies. The high frequency parts are eliminated by neglecting some of the inertia forces and torques. This reduces numerical stiffness and allows larger step-sizes for the time integration.

The efficient and real-time capable combination with existing highly efficient algorithms for multi-body dynamics (\(\mathcal{O}(N)\) multi-body formalisms) requires appropriate integration methods that are adapted to the special structure of the multi-body formalism and solve the nonlinear constraints with a small, limited number of calculation steps.


Model reduction Equations of motion Quasi-static Multi-body formalism 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Bernhard Burgermeister
    • 1
  • Martin Arnold
    • 2
  • Alexander Eichberger
    • 1
  1. 1.SIMPACK AGGilchingGermany
  2. 2.NWF II-Institute of MathematicsMartin Luther University Halle-WittenbergHalle (Saale)Germany

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