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非完整约束Hamilton动力系统保结构算法

满淑敏 高强 钟万勰

满淑敏, 高强, 钟万勰. 非完整约束Hamilton动力系统保结构算法[J]. 应用数学和力学, 2020, 41(6): 581-590. doi: 10.21656/1000-0887.400375
引用本文: 满淑敏, 高强, 钟万勰. 非完整约束Hamilton动力系统保结构算法[J]. 应用数学和力学, 2020, 41(6): 581-590. doi: 10.21656/1000-0887.400375
MAN Shumin, GAO Qiang, ZHONG Wanxie. A StructurePreserving Algorithm for Hamiltonian Systems With Nonholonomic Constraints[J]. Applied Mathematics and Mechanics, 2020, 41(6): 581-590. doi: 10.21656/1000-0887.400375
Citation: MAN Shumin, GAO Qiang, ZHONG Wanxie. A StructurePreserving Algorithm for Hamiltonian Systems With Nonholonomic Constraints[J]. Applied Mathematics and Mechanics, 2020, 41(6): 581-590. doi: 10.21656/1000-0887.400375

非完整约束Hamilton动力系统保结构算法

doi: 10.21656/1000-0887.400375
基金项目: 国家自然科学基金(11972107;91748203);中央高校基本科研业务费(DUT2019TD37)
详细信息
    作者简介:

    满淑敏(1990—),女,博士生(E-mail: manshumin@mail.dlut.edu.cn);高强(1978—),男,教授,博士生导师(通讯作者. E-mail: qgao@dlut.edu.cn).

  • 中图分类号: O241

A StructurePreserving Algorithm for Hamiltonian Systems With Nonholonomic Constraints

Funds: The National Natural Science Foundation of China(11972107;91748203)
  • 摘要: 基于变分积分的思想和对偶变量表示的Lagrange-d’Alembert原理,构造了一类求解非完整约束Hamilton动力系统的高阶保结构算法.基于变分积分法,选取适当的多项式及数值积分方法,将对偶变量形式的Lagrange-d’Alembert原理进行离散.在此离散原理的基础上,以积分区间两端位移为独立变量,同时要求在区间端点处及区间内部的控制点处严格满足非完整约束,从而得到数值积分方法.给出了算法的对称性证明.数值算例表明算法具有高阶收敛性,严格满足非完整约束,且在长时间仿真后,依然能保持良好的数值性质.
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出版历程
  • 收稿日期:  2019-12-23
  • 刊出日期:  2020-06-01

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