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一种避开大转动奇异点的角速度数值积分方法

张志刚 侯俊剑 齐朝晖

张志刚, 侯俊剑, 齐朝晖. 一种避开大转动奇异点的角速度数值积分方法[J]. 应用数学和力学, 2018, 39(4): 452-461. doi: 10.21656/1000-0887.380222
引用本文: 张志刚, 侯俊剑, 齐朝晖. 一种避开大转动奇异点的角速度数值积分方法[J]. 应用数学和力学, 2018, 39(4): 452-461. doi: 10.21656/1000-0887.380222
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
Citation: 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

一种避开大转动奇异点的角速度数值积分方法

doi: 10.21656/1000-0887.380222
基金项目: 国家自然科学基金(11602228;51505433)
详细信息
    作者简介:

    张志刚(1984—),男,讲师,博士(通讯作者. E-mail: zhigangzhang@foxmail.com).

  • 中图分类号: O302

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

Funds: The National Natural Science Foundation of China(11602228;51505433)
  • 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.
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出版历程
  • 收稿日期:  2017-08-04
  • 修回日期:  2017-10-06
  • 刊出日期:  2018-04-15

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