On Baumgarte Stabilization for Differential Algebraic Equations

  • Georg-P. Ostermeyer
Part of the NATO ASI Series book series (volume 69)


Baumgarte’s method uses analytical reformulations of constraint forces in mechanical systems to handle differential algebraic equations with every standard integration routine. This stabilization technique for inner and outer constraints is easy to use.

This paper deals with control theoretic aspects to explain the effects of Baumgarte’s method and to give some rules for choosing the parameters in his technique. In addition the construction of new stabilizing procedures is described and some optimal formulas are listed at the end of this paper.


Constraint Equation Multibody System Constraint Force Differential Algebraic Equation Nonholonomic Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Baumgarte, J.: Stabilization of constraints and integrals of motion in dynamical systems. Comp. Meth. in Appl. Mech. and Eng. 1 (1972), 1–16.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Roberson, R.E.: Constraint stabilization for rigid bodies: an extension of Baumgarte1s method, IUTAM Symp. on Dynamics of multibody systems, Munich 29.8.–39.77,Berlin Springer Verlag 1978, S. 274–290.Google Scholar
  3. 3.
    Grünhagen, W.v.: Zur Stabilisierung der numerischen Integration von Bewegungsgleichungen. Diss. TU Braunschweig, DFVLR - FB79 - 41.Google Scholar
  4. 4.
    Geiger, W.: Numerische Instabilität und Stabilisierung der kinematischen Quaternionengleichung. ZAMM 59 (1979), T118–T120Google Scholar
  5. 5.
    Wittenburg, J.: Dynamics of multibody systems, IUTAM Symp. on Theor. and appl. Mechanics, Toronto 17.8.–23.8. 1980, North Holland Publ. Comp. 1981, S 11–22.Google Scholar
  6. 6.
    Ostermeyer, G.P.: Mechanische Systeme mit beschränktem Konfigurationsraum, Diss. TU Braunschweig 1983.Google Scholar
  7. 7.
    Nikravesh, P.E.: Some methods for dynamic analysis of constrained mechanical systems: a survey. In E. Haug (ed.), Computer aided analysis and optimization of mechanical system dynamics, Springer-Verlag 1984.Google Scholar
  8. 8.
    Baumgarte,J., Ostermeyer, G.P.: Quasigeneralisierte Variable. ZAMM 65 (1985) 10, 417–478.Google Scholar
  9. 9.
    Petzold, L.R., Lötstedt,P.: Numerical solution of nonlinear differential equations with algebraic constraints II:Practical Implications. SIAM J. Sei. Stat. Comput., 7, 3, 1986, S. 720–733MathSciNetGoogle Scholar
  10. 10.
    Führer, C.: Differential - algebraische Gleichungssysteme in mechanischen Mehrkörpersystemen, Theorie, num.Ansätze und Anwendungen., Diss. TU München, 1988.Google Scholar
  11. 11.
    Knorrenschild, M.: Regularisierung von Differentie11-algebraischen Systemen - theoretische und numerische Aspekte. Diss. TH Aachen, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Georg-P. Ostermeyer
    • 1
  1. 1.Volkswagen AGWolfsburgGermany

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