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广义算子下约束Hamilton系统的Noether定理

沈世磊 宋传静

沈世磊,宋传静. 广义算子下约束Hamilton系统的Noether定理 [J]. 应用数学和力学,2022,43(12):1422-1433 doi: 10.21656/1000-0887.430091
引用本文: 沈世磊,宋传静. 广义算子下约束Hamilton系统的Noether定理 [J]. 应用数学和力学,2022,43(12):1422-1433 doi: 10.21656/1000-0887.430091
SHEN Shilei, SONG Chuanjing. Noether’s Theorem for Constrained Hamiltonian System Under Generalized Operators[J]. Applied Mathematics and Mechanics, 2022, 43(12): 1422-1433. doi: 10.21656/1000-0887.430091
Citation: SHEN Shilei, SONG Chuanjing. Noether’s Theorem for Constrained Hamiltonian System Under Generalized Operators[J]. Applied Mathematics and Mechanics, 2022, 43(12): 1422-1433. doi: 10.21656/1000-0887.430091

广义算子下约束Hamilton系统的Noether定理

doi: 10.21656/1000-0887.430091
基金项目: 国家自然科学基金(12172241;12272248;11972241;11802193);江苏省自然科学基金(BK20191454);江苏省高校“青蓝工程”项目
详细信息
    作者简介:

    沈世磊(1998—),男,硕士(E-mail:2569147446@qq.com

    宋传静(1987—),女,副教授,博士(通讯作者. E-mail:songchuanjingsun@126.com

  • 中图分类号: O316

Noether’s Theorem for Constrained Hamiltonian System Under Generalized Operators

  • 摘要:

    研究了广义算子下奇异系统的Noether对称性与守恒量。首先,建立了广义算子下奇异系统的Lagrange方程,并导出该系统的初级约束,然后引入Lagrange乘子建立了广义算子下约束Hamilton方程以及相容性条件。其次,基于Hamilton作用量在无限小变换下的不变性,建立了广义算子下约束Hamilton系统的Noether定理,并给出了该系统的对称性及相应的守恒量。在特定条件下,广义算子下约束Hamilton系统的Noether守恒量可以退化为整数阶约束Hamilton系统的Noether守恒量。最后举例说明了结果的应用。

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出版历程
  • 收稿日期:  2022-03-21
  • 修回日期:  2022-04-14
  • 网络出版日期:  2022-12-20
  • 刊出日期:  2022-12-01

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