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On the optimal scaling of index three DAEs in multibody dynamics

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Abstract

We propose a preconditioning strategy for the governing equations of multibody systems in index-3 differential-algebraic form. The method eliminates the amplification of errors and the ill-conditioning which affect numerical solutions of high index differential algebraic equations for small time steps. We develop a new theoretical analysis of the perturbation problem and we apply it to the derivation of preconditioners for the Newmark family of integration schemes. The theoretical results are confirmed by numerical experiments.

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Authors and Affiliations

  1. Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa 34, 20156, Milano, Italy

    Carlo L. Bottasso & Lorenzo Trainelli

  2. Escuela Politécnica Superior, University of La Coruña, Mendizábal s/n, 15403, Ferrol, Spain

    Daniel Dopico

Authors
  1. Carlo L. Bottasso
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  2. Daniel Dopico
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  3. Lorenzo Trainelli
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Correspondence to Carlo L. Bottasso.

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Bottasso, C.L., Dopico, D. & Trainelli, L. On the optimal scaling of index three DAEs in multibody dynamics. Multibody Syst Dyn 19, 3–20 (2008). https://doi.org/10.1007/s11044-007-9051-9

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  • DOI: https://doi.org/10.1007/s11044-007-9051-9

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