Numerische Mathematik

, Volume 129, Issue 1, pp 149–179 | Cite as

Error analysis of generalized-\(\alpha \) Lie group time integration methods for constrained mechanical systems



Generalized-\(\alpha \) methods are very popular in structural dynamics. They are methods of Newmark type and combine favourable stability properties with second order convergence for unconstrained second order systems in linear spaces. Recently, they were extended to constrained systems in flexible multibody dynamics that have a configuration space with Lie group structure. In the present paper, the convergence of these Lie group methods is analysed by a coupled one-step error recursion for differential and algebraic solution components. It is shown that spurious oscillations in the transient phase result from order reduction that may be avoided by a perturbation of starting values or by index reduction. Numerical tests for a benchmark problem from the literature illustrate the results of the theoretical investigations.

Mathematics Subject Classification

65L80 65L20 70H45 70F20 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Martin Arnold
    • 1
  • Olivier Brüls
    • 2
  • Alberto Cardona
    • 3
  1. 1.Institute of MathematicsMartin Luther University Halle-WittenbergHalle (Saale)Germany
  2. 2.Department of Aerospace and Mechanical Engineering (LTAS)University of LiègeLiègeBelgium
  3. 3.CIMEC, Universidad Nacional del Litoral, ConicetSanta FeArgentina

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