An Improved Symplectic Integration for Rigid Body Dynamics in Terms of Unit Quaternions

XU Xiao-ming; ZHONG Wan-xie

doi:10.3879/j.issn.1000-0887.2014.11.001

Volume 35 Issue 11

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XU Xiao-ming, ZHONG Wan-xie. An Improved Symplectic Integration for Rigid Body Dynamics in Terms of Unit Quaternions[J]. Applied Mathematics and Mechanics, 2014, 35(11): 1177-1187. doi: 10.3879/j.issn.1000-0887.2014.11.001

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An Improved Symplectic Integration for Rigid Body Dynamics in Terms of Unit Quaternions

doi: 10.3879/j.issn.1000-0887.2014.11.001

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

Funds: The National Natural Science Foundation of China(General Program)(11472067)

Received Date: 2014-06-26
Rev Recd Date: 2014-09-11
Publish Date: 2014-11-18

Abstract

Abstract

An identity transformation between the time derivative of quaternions and angular velocity was introduced into the kinetic energy term, according to the theory of quaternionbased rigid body dynamics. This proposed approach yielded a nonsingular mass matrix. Combined with the analytical structural mechanics, a new symplectic integration scheme with 4 formulations, was proposed. In practice, the discrete variational principle of the action function was employed to replace the relevant quaternion differential equations for the proposed method. Correspondingly, the unit length constraint was met explicitly by means of the algebraic constraint at the integration grid points. The numerical results show that the new scheme avoids the severe periodical nutation errors for the special cases of steady precession of a gyro top, which is a puzzling phenomenon in recent researches. In addition, the new scheme presents an impressive improvement of accuracy for the general cases as well.
- analytical structural mechanics,
- unit quaternion,
- rigid body dynamics,
- symplectic integration,
- identity transformation,
- heavy top

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References(14)

References

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