Journal of Mechanical Science and Technology

, Volume 29, Issue 7, pp 2579–2585 | Cite as

Order reduction in time integration caused by velocity projection



Holonomic constraints restrict the configuration of a multibody system to a subset of the configuration space. They imply so called hidden constraints at the level of velocity coordinates that may formally be obtained from time derivatives of the original holonomic constraints. A numerical solution that satisfies hidden constraints as well as the original constraint equations may be obtained considering both types of constraints simultaneously in each time step (Stabilized index-2 formulation) or using projection techniques. Both approaches are well established in the time integration of differential-algebraic equations. Recently, we have introduced a generalized-α Lie group time integration method for the stabilized index-2 formulation that achieves second order convergence for all solution components. In the present paper, we show that a separate velocity projection would be less favourable since it may result in an order reduction and in large transient errors after each projection step. This undesired numerical behaviour is analysed by a one-step error recursion that considers the coupled error propagation in differential and algebraic solution components. This one-step error recursion has been used before to prove second order convergence for the application of generalized-α methods to constrained systems.


Generalized-α method Lie group time integration Velocity projection 


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Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

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

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