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本文引用格式:张毅.时间尺度上约束Birkhoff系统的Noether对称性与守恒量[J].动力学与控制学报,2019,17(5):482~486;   Zhang Yi.Noether symmetries and conserved quantities of constrained Birkhoffian systems on time scales[J].Journal of Dynamics and Control,2019,17(5):482-486.
时间尺度上约束Birkhoff系统的Noether对称性与守恒量    点此下载全文
张毅
苏州科技大学 土木工程学院, 苏州 215011)
基金项目:国家自然科学基金资助项目(11572212,11272227,11972241)
DOI:10.6052/1672-6553-2019-062
摘要:
      研究时间尺度上约束Birkhoff系统的Noether对称性.基于时间尺度上Pfaff Birkhoff原理,建立了时间尺度上带乘子形式的约束Birkhoff方程.〖JP2〗给出了时间尺度上的Noether等式,定义了时间尺度上约束Birkhoff系统Noether对称性.〖JP〗提出并证明了时间尺度上约束Birkhoff系统的Noether定理,该定理揭示了时间尺度上Noether对称性与守恒量之间的关系.给出定理的两个特例:时间尺度上Birkhoff系统和经典约束Birkhoff系统的Noether定理.文末给出算例以说明方法和结果的有效性.
关键词:约束Birkhoff系统,时间尺度,Noether对称性,守恒量
Noether symmetries and conserved quantities of constrained Birkhoffian systems on time scales    Download Fulltext
Zhang Yi
Fund Project:
Abstract:
      The Noether symmetries of constrained Birkhoffian systems on time scales were studied. Based on the principle of Pfaff Birkhoff on time scales, the Birkhoff′s equations with multipliers on time scales for a constrained Birkhoffian system were established. The Noether identity on time scales was given, and the Noether symmetry of the constrained Birkhoffian system on time scales was defined. The Noether′s theorem of the constrained Birkhoffian system on time scales was proposed and proved, which revealed the relationship between the Noether symmetry and conserved quantity. Two special cases of the Noether′s theorem were given for a free Birkhoffian system on time scales and a classical constrained Birkhoffian system. Finally, a numerical example was presented to illustrate the effectiveness of this method.
Keywords:constrained Birkhoffian system,time scale,Noether symmetry,conserved quantity
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