BAI Long, DONG Zhi-feng, GE Xin-sheng. Lie Group and Lie Algebra Modeling for Numerical Calculation of Rigid Body Dynamics[J]. Applied Mathematics and Mechanics, 2015, 36(8): 833-843. doi: 10.3879/j.issn.1000-0887.2015.08.005
Citation: BAI Long, DONG Zhi-feng, GE Xin-sheng. Lie Group and Lie Algebra Modeling for Numerical Calculation of Rigid Body Dynamics[J]. Applied Mathematics and Mechanics, 2015, 36(8): 833-843. doi: 10.3879/j.issn.1000-0887.2015.08.005

Lie Group and Lie Algebra Modeling for Numerical Calculation of Rigid Body Dynamics

doi: 10.3879/j.issn.1000-0887.2015.08.005
Funds:  The National Natural Science Foundation of China(11472058)
  • Received Date: 2015-01-30
  • Rev Recd Date: 2015-06-20
  • Publish Date: 2015-08-15
  • The Lie group dynamics equation for rigid bodies was derived based on the exponent mapping equivalence relationship between the Lie group and Lie algebra. The discrete Lie group variational integrator was derived according to the discrete variation theory. The momentum conservation of the 2 Lie group equations was demonstrated. The Lie group dynamics equation was processed so that every part has the same dimension and the equation can be solved with the RungeKutta method directly. The RungeKutta method to directly solve the Lie group dynamics equation with different dimensions was also built. The Lie group variational integrator was solved with the Lie algebraic transform, the Cayley transform and Newton iteration, respectively. The computation results of the 3 algorithms are highly identical to each other, the structure conservation and momentum conservation both have high precisions.
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