Noether’s Theorem for Constrained Hamiltonian System Under Generalized Operators北大核心CSCD |
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引用本文: | 沈世磊,宋传静.Noether’s Theorem for Constrained Hamiltonian System Under Generalized Operators北大核心CSCD[J].应用数学和力学,2022,43(12):1422-1433. |
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作者姓名: | 沈世磊 宋传静 |
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作者单位: | 苏州科技大学 数学科学学院,江苏 苏州 215009 |
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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 |
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摘 要: | Noether’s symmetry and conserved quantity of singular systems under generalized operators were studied. Firstly, the Lagrangian equation of singular systems under generalized operators was established, and the primary constraints on the system were derived. Then the Lagrangian multiplier was introduced to establish the constrained Hamilton equation and the compatibility condition under generalized operators. Secondly, based on the invariance of the Hamilton action under the infinitesimal transformation, Noether’s theorem for constrained Hamiltonian systems under generalized operators was established, and the symmetry and corresponding conserved quantity of the system were given. Under certain conditions, Noether’s conservation of constrained Hamiltonian systems under generalized operators can be reduced to Noether’s conservation of integer-order constrained Hamiltonian systems. Finally, an example illustrates the application of the results. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.
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关 键 词: | 广义算子 奇异系统 初级约束 约束Hamilton方程 Noether定理 对称性与守恒量 |
收稿时间: | 2022-03-21 |
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