Symplectic Integration for Multibody Dynamics Based on Quaternion Parameters

XU Xiao-ming; ZHONG Wan-xie

doi:10.3879/j.issn.1000-0887.2014.10.001

Volume 35 Issue 10

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XU Xiao-ming, ZHONG Wan-xie. Symplectic Integration for Multibody Dynamics Based on Quaternion Parameters[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1071-1080. doi: 10.3879/j.issn.1000-0887.2014.10.001

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Symplectic Integration for Multibody Dynamics Based on Quaternion Parameters

doi: 10.3879/j.issn.1000-0887.2014.10.001

State Key Laboratory of Structural Analysis for Industrial Equipment(Dalian University of Technology); Department of Engineering Mechanics,Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Received Date: 2014-06-25
Rev Recd Date: 2014-08-20
Publish Date: 2014-10-15

Abstract

Abstract

The quaternion representation was introduced into multibody dynamics for the description of rigid body rotation, based on which the constrained dynamics was derived and the relevant Lagrange system was established. Then, the segmental action for discrete systems was introduced and approximated with the finite element method. According to the theory of analytical structural mechanics, the symplectic numerical integration was derived with the constraints strictly satisfied at the integration points and the integration process was symplectic conservative in the sense of variation principle. The proposed method has the characteristics of less calculation and less unknown numbers, which is confirmed with the numerical results of an exemplary multibody hinged system.
- analytical structural mechanics,
- quaternion,
- multibody dynamics,
- symplectic integration

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References(9)

References

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