Multibody System Dynamics

, Volume 22, Issue 3, pp 297–319 | Cite as

Implementation of consequent stabilization method for simulation of multibodies described in absolute coordinates

  • Dmitry VlasenkoEmail author
  • Roland Kasper


In this article, we propose methods that increase numerical efficiency of dynamic simulation of spatial multibody systems described in absolute coordinates. The successive coordinate projection method efficiently stabilizes the system constraints in the case when a non-minimal set of orientation coordinates is used to describe the orientation of bodies in space. The new procedure of generation of Newton–Euler equations is shown in detail for systems with the most popular types of joints (prismatic joint, revolute joint, etc.). The proposed algorithms were tested with models of a governor mechanism and Yamaha YZF-R1 motorcycle engine. The simulation results show that the successive coordinate projection method is stable and can be implemented for complex mechanical systems.


Projection Dynamics Multibody Euler parameters 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ascher, U., Chin, H., Petzold, L., Reich, S.: Stabilization of constrained mechanical systems with DAEs and invariant manifolds. Mech. Struct. Mach. 23, 135–157 (1995) CrossRefMathSciNetGoogle Scholar
  2. 2.
    Baumgarte, J.: Stabilization of constraints and integrals of motion in dynamical systems. Comput. Methods Appl. Mech. Eng. 1, 1–16 (1972) zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Blajer, W.: A geometric unification of constrained system dynamics. Multibody Syst. Dyn. 1, 3–21 (1997) zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Blajer, W.: Elimination of constraint violation and accuracy aspects in numerical simulation of multibody systems. Multibody Syst. Dyn. 7, 265–284 (2002) zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Chin, H.: Stabilization methods for simulations of constrained multibody dynamics. PhD thesis, University of British Columbia, Vancouver, Canada (1995) Google Scholar
  6. 6.
    Eich-Soellner, E., Führer, C.: Numerical Methods in Multibody Dynamics. Teubner, Stuttgart (1998) zbMATHGoogle Scholar
  7. 7.
    Eich, E.: Projizierende Mehrschrittverfahren zur numerischen Losung der Bewegungsgleichungen technischer Mehrkorpersysteme mit Zwangsbedingungen und Unstetigkeiten. PhD thesis, Institut für Mathematik, Universität Augsburg. “VDI-Fortschrittsberichte”, Reihe 18, Nr. 109,VDI-Verlag, Düsseldorf (1992) Google Scholar
  8. 8.
    Ferguson, C.R.: Internal Combustion Engines. Applied Thermosciences, 1st edn. Wiley, New York (1986) Google Scholar
  9. 9.
    Jalon, G., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems. Springer, Berlin (1994) Google Scholar
  10. 10.
    Haug, E.J.: Computer Aided Kinematics and Dynamics of Mechanical Systems, vol. I: Basic Methods. Allyn & Bacon, Boston (1989) Google Scholar
  11. 11.
    Heywood, J.B.: Internal Combustion Engine Fundamentals, p. 435. McGraw-Hill, New York (1988) Google Scholar
  12. 12.
    Hopf, H.: Systeme symmetrischer Bilinearformen und Euklidische Modelle der projektiven Räume. Naturf. Ges., Zürich, S. 165–177 (1940) Google Scholar
  13. 13.
    Kasper, R., Vlasenko, D., Sintotskiy, G.: A component oriented approach to multidisciplinary simulation of mechatronic systems. In: Proceedings of the EUROSIM congress on Modelling and Simulation (EUROSIM 2007), Ljubljana, Slovenia, September 9–13, 2007 Google Scholar
  14. 14.
    Schwab, A.L., Meijaard, J.P.: How to draw Euler angles and utilize Euler parameters. In: Proceedings of IDETC/CIE 2006, ASME 2006 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Philadelphia, PA, September 10–13, 2006. ASME, New York (2006). CD-ROM Google Scholar
  15. 15.
    Schwerin, R.: Multibody System Simulation. Numerical Methods, Algorithms and Software. Springer, Berlin (1999) zbMATHGoogle Scholar
  16. 16.
    Shabana, A.A.: Computational Dynamics. Wiley, New York (2001) Google Scholar
  17. 17.
    Stuelpnagel, J.: On the parameterization of the three-dimensional rotation group. SIAM Rev. 6(4), 422–430 (1964) zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Vlasenko, D., Kasper, R.: A new software approach for the simulation of multibody dynamics. ASME J. Comput. Nonlinear Dyn. 2(3), 274–278 (2007) CrossRefGoogle Scholar
  19. 19.
    Vlasenko, D., Kasper, R.: Implementation of the Symbolic Simplification for the Calculation of Accelerations of Multibodies. In: Proceedings of Industrial Simulation Conference 2008, Lyon, France, June 9–11, 2008 Google Scholar
  20. 20.
    Wittenburg, J.: Dynamics of Multibody Systems. Springer, Berlin (2008) zbMATHGoogle Scholar
  21. 21.
    Yoon, S., Howe, R.M., Greenwood, D.T.: Geometric elimination of constraint violations in numerical simulation of Lagrangian equations. Trans. ASME, J. Mech. Des. 116, 1058–1064 (1994) CrossRefGoogle Scholar
  22. 22.
    YZF-R1P/YZF-R1PC Service Manual, 1st edn. Yamaha Motor Corporation, USA (2001) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institute of Mobile Systems (IMS)Otto-von-Guericke-University MagdeburgMagdeburgGermany

Personalised recommendations