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Xiuteng Ma Yanbo Zhai Shuqiang Luo. Numerical method of multibody dynamics based on \theta _1 method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(5): 931-938. DOI: 10.6052/0459-1879-2011-5-lxxb2010-730
Citation: Xiuteng Ma Yanbo Zhai Shuqiang Luo. Numerical method of multibody dynamics based on \theta _1 method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(5): 931-938. DOI: 10.6052/0459-1879-2011-5-lxxb2010-730

Numerical method of multibody dynamics based on \theta _1 method

  • Received Date: November 02, 2010
  • Revised Date: April 06, 2011
  • In the numerical integration of ordinary differentialequations (ODEs) in structural dynamics community, \theta _1 method hascharacteristics of controlled numerical dissipation and second-orderaccuracy for systems with or without physical damping. Based on thesecharacteristics, \theta _1 method is extended to the numerical integrationof motion equations in multibody system dynamics. The solved motionequations are index-3 differential-algebraic equations (DAEs) andindex-2 over-determined DAEs (ODAEs). Numerical experiments validate the\theta_1 method, experiments also show the relationship of numericaldissipation with parameter \theta_1.As for theintegration of index-3 DAEs by \theta _1 method, it has violation ofvelocity constraint, while for index-2 ODAEs, there are no violation ofposition and velocity constraint in the view of computer precision. Inaddition, experiments illustrate that, for non-conservative system motionequations in the form of index-3 DAEs and index-2 ODAEs, \theta _1 methodhas second-order accuracy. In the end, \theta _1 methods for motionequations are compared with other direct-time integrations from the CPU timepoint of view.
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