## 留言板

 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
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.

• 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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