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多体系统动力学微分-代数方程L-稳定方法

李博文 丁洁玉 李亚男

李博文, 丁洁玉, 李亚男. 多体系统动力学微分-代数方程L-稳定方法[J]. 应用数学和力学, 2019, 40(7): 768-779. doi: 10.21656/1000-0887.400038
引用本文: 李博文, 丁洁玉, 李亚男. 多体系统动力学微分-代数方程L-稳定方法[J]. 应用数学和力学, 2019, 40(7): 768-779. doi: 10.21656/1000-0887.400038
LI Bowen, DING Jieyu, LI Yanan. An L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics[J]. Applied Mathematics and Mechanics, 2019, 40(7): 768-779. doi: 10.21656/1000-0887.400038
Citation: LI Bowen, DING Jieyu, LI Yanan. An L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics[J]. Applied Mathematics and Mechanics, 2019, 40(7): 768-779. doi: 10.21656/1000-0887.400038

多体系统动力学微分-代数方程L-稳定方法

doi: 10.21656/1000-0887.400038
基金项目: 国家自然科学基金(11472143;11772166)
详细信息
    作者简介:

    李博文(1995―),女,硕士生(E-mail: 1032788712@qq.com);丁洁玉(1978―),女,教授,博士,博士生导师(通讯作者. E-mail: djy@qdu.edu.cn).

  • 中图分类号: TP301.6;O175.1

An L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics

Funds: The National Natural Science Foundation of China(11472143;11772166)
  • 摘要: 针对多体系统动力学微分-代数方程形式,在时间区间上构造L-稳定方法,分别基于等距节点、Chebyshev节点和Legendre节点等非等距节点建立求解格式,依据Ehle定理及猜想,与Padé逼近式对比得到待定矩阵和向量,从而获得L-稳定求解公式,循环求解过程采用Newton迭代法计算.以平面双连杆机械臂系统为例,使用L-稳定方法进行数值仿真,通过改变时间区间节点数和步长对各个指标结果进行比较,并与经典Runge-Kutta法对比.结果表明,该方法具有稳定性好、精度高等优点,适用于长时间情况下的多体系统动力学仿真.
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出版历程
  • 收稿日期:  2019-01-17
  • 修回日期:  2019-02-09
  • 刊出日期:  2019-07-01

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