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时滞Lagrange系统的Lie对称性与守恒量研究

郑明亮

郑明亮. 时滞Lagrange系统的Lie对称性与守恒量研究 [J]. 应用数学和力学,2021,42(11):1161-1168 doi: 10.21656/1000-0887.410184
引用本文: 郑明亮. 时滞Lagrange系统的Lie对称性与守恒量研究 [J]. 应用数学和力学,2021,42(11):1161-1168 doi: 10.21656/1000-0887.410184
ZHENG Mingliang. Lie Symmetries and Conserved Quantities of Lagrangian Systems With Time Delays[J]. Applied Mathematics and Mechanics, 2021, 42(11): 1161-1168. doi: 10.21656/1000-0887.410184
Citation: ZHENG Mingliang. Lie Symmetries and Conserved Quantities of Lagrangian Systems With Time Delays[J]. Applied Mathematics and Mechanics, 2021, 42(11): 1161-1168. doi: 10.21656/1000-0887.410184

时滞Lagrange系统的Lie对称性与守恒量研究

doi: 10.21656/1000-0887.410184
基金项目: 江苏省高等学校自然科学基金(20KJD460001)
详细信息
    作者简介:

    郑明亮(1988—),男,副教授,博士(E-mail:zhmlwxcstu@163.com)

  • 中图分类号: O316; O322

Lie Symmetries and Conserved Quantities of Lagrangian Systems With Time Delays

  • 摘要: 研究了位形间中含单时滞参数的非保守力学系统的Lie对称性和守恒量。首先,利用含时滞的动力学Hamilton原理,建立了含时滞的非保守系统的分段Lagrange运动方程;其次,利用微分方程容许Lie群理论,得到系统的Lie对称确定方程;然后,根据对称性与守恒量之间的关系,通过构造结构方程,得到含时滞的非保守系统的Lie定理;最后,给出了两个具体的算例说明了方法的应用。结果表明:时滞参数的存在使非保守系统的Lagrange方程呈现分段特性,相应的Lie对称性确定方程的个数应是自由度数目的2倍,这对生成元函数提出了更高的限制,同时,守恒量呈现依赖速度项的分段表达。
  • 图  1  时滞弹簧振子模型

    Figure  1.  The spring oscillator model with time delay

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出版历程
  • 收稿日期:  2020-06-23
  • 修回日期:  2020-12-23
  • 网络出版日期:  2021-12-07
  • 刊出日期:  2021-11-30

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