A Numerical Integration Method for Angular Velocity Vectors to Avoid Singularity of Large Rotation

ZHANG Zhigang; HOU Junjian; QI Zhaohui

doi:10.21656/1000-0887.380222

Volume 39 Issue 4

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Article Navigation > Applied Mathematics and Mechanics > 2018 > 39(4): 452-461

ZHANG Zhigang, HOU Junjian, QI Zhaohui. A Numerical Integration Method for Angular Velocity Vectors to Avoid Singularity of Large Rotation[J]. Applied Mathematics and Mechanics, 2018, 39(4): 452-461. doi: 10.21656/1000-0887.380222

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A Numerical Integration Method for Angular Velocity Vectors to Avoid Singularity of Large Rotation

doi: 10.21656/1000-0887.380222

¹Mechanical and Electrical Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, P.R.China;²School of State Key Laboratory of Structural Analysis for Industrial Equipment(Dalian University of Technology ), Dalian, Liaoning 116023, P.R.China

Funds: The National Natural Science Foundation of China（11602228;51505433）

Received Date: 2017-08-04
Rev Recd Date: 2017-10-06
Publish Date: 2018-04-15

Abstract

Abstract

Using 3 parameters to describe finite rotations will inevitably have the singularity problem, which leads to numerical difficulties in solving the rotational parameters from the integration of the angular velocity. Based on systematical studies of the singularity of the rotation vector, a new numerical integration method, which can overcome singular points of the rotation vector, was proposed. With the property that the 2 rotation vectors with the same direction but different norms correspond to the same finite rotation, the rotation vector near the singular point was switched to its corresponding one far away from the singular point and in the numerical stability region, during the numerical integration. This method can avoid the difficulties in the numerical integration caused by the singularity of rotation vectors for the angular velocity vectors. Numerical examples show that the proposed method is simple, stable and effective.
- finite rotation,
- rotation vector,
- singularity,
- angular velocity vector,
- numerical integration

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References(18)

References

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