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变加速动力学系统的广义高斯最小拘束原理

张毅 宋传静 翟相华

张毅, 宋传静, 翟相华. 变加速动力学系统的广义高斯最小拘束原理. 力学学报, 2023, 55(5): 1-7 doi: 10.6052/0459-1879-23-030
引用本文: 张毅, 宋传静, 翟相华. 变加速动力学系统的广义高斯最小拘束原理. 力学学报, 2023, 55(5): 1-7 doi: 10.6052/0459-1879-23-030
Zhang Yi, Song Chuanjing, Zhai Xianghua. Generalized Gauss principle of least compulsion for variable-acceleration dynamical systems. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(5): 1-7 doi: 10.6052/0459-1879-23-030
Citation: Zhang Yi, Song Chuanjing, Zhai Xianghua. Generalized Gauss principle of least compulsion for variable-acceleration dynamical systems. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(5): 1-7 doi: 10.6052/0459-1879-23-030

变加速动力学系统的广义高斯最小拘束原理

doi: 10.6052/0459-1879-23-030
基金项目: 国家自然科学基金资助项目(12272248, 11972241, 12172241, 12002228)
详细信息
    通讯作者:

    张毅, 教授, 主要研究方向为分析力学. E-mail: zhy@mail.usts.edu.cn

    翟相华, 讲师, 主要研究方向为分析力学. E-mail: zxh@mail.usts.edu.cn

  • 中图分类号: O316

GENERALIZED GAUSS PRINCIPLE OF LEAST COMPULSION FOR VARIABLE-ACCELERATION DYNAMICAL SYSTEMS

  • 摘要: 变加速运动在日常生活和工程问题中普遍存在. 变加速动力学又称牛顿猝变动力学, 因其在混沌理论和非线性动力学中的应用而获得广泛关注. 高斯原理是一个具有极值性质的微分变分原理. 因此, 研究变加速动力学系统的广义高斯原理在理论和应用两方面都有重要意义. 文章提出并研究变加速动力学系统的广义高斯原理. 首先, 引入急动度空间的广义高斯变分概念, 将质点的达朗贝尔原理对时间求导数后与广义高斯变分点乘, 并利用高斯意义下的理想约束条件, 建立了变加速动力学系统的广义高斯原理. 在此基础上, 通过构造广义拘束函数建立并证明变加速动力学系统的广义高斯最小拘束原理, 并给出原理的阿佩尔形式、拉格朗日形式和尼尔森形式. 其次, 研究原理对变质量力学的推广. 从密歇尔斯基方程出发, 将它对时间求导并与广义高斯变分点乘, 建立了具有理想约束的变质量变加速动力学系统的广义高斯原理. 通过构造变质量系统的广义拘束函数, 建立并证明变质量力学系统变加速运动的广义高斯最小拘束原理. 文中以开普勒−牛顿空间问题为例, 利用所得的广义高斯最小拘束原理方法进行计算, 验证了方法的有效性.

     

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  • 收稿日期:  2023-02-01
  • 录用日期:  2023-03-07
  • 网络出版日期:  2023-03-08

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