A Numerical Integration Method for Angular Velocity Vectors to Avoid Singularity of Large Rotation
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摘要: 采用三参数描述有限转动会不可避免的遇到奇异性问题,这给由角速度积分求解转动参数带来了数值困难.系统地研究了采用转动矢量描述空间大转动的奇异性问题,在此基础上提出了一种避开转动矢量奇异点的数值积分方法.利用方向相同、模相差2π的两个转动矢量对应同一有限转动这一性质,在数值积分过程中将靠近奇异点的转动矢量切换到与之对应但远离奇异点的数值稳定区,从而避开了转动矢量奇异性给角速度数值积分带来的困难.数值算例表明所提方法简单、稳定、有效.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.
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Key words:
- finite rotation /
- rotation vector /
- singularity /
- angular velocity vector /
- numerical integration
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