舒莲莲, 朱建青. 时间尺度上Whittaker方程的Noether对称性与守恒量[J]. 云南大学学报(自然科学版), 2022, 44(6): 1166-1173. doi: 10.7540/j.ynu.20210217
引用本文: 舒莲莲, 朱建青. 时间尺度上Whittaker方程的Noether对称性与守恒量[J]. 云南大学学报(自然科学版), 2022, 44(6): 1166-1173. doi: 10.7540/j.ynu.20210217
SHU Lian-lian, ZHU Jian-qing. On Noether symmetries and conserved quantities of Whittaker equations on time scales[J]. Journal of Yunnan University: Natural Sciences Edition, 2022, 44(6): 1166-1173. DOI: 10.7540/j.ynu.20210217
Citation: SHU Lian-lian, ZHU Jian-qing. On Noether symmetries and conserved quantities of Whittaker equations on time scales[J]. Journal of Yunnan University: Natural Sciences Edition, 2022, 44(6): 1166-1173. DOI: 10.7540/j.ynu.20210217

时间尺度上Whittaker方程的Noether对称性与守恒量

On Noether symmetries and conserved quantities of Whittaker equations on time scales

  • 摘要: 研究时间尺度上Whittaker方程的Noether对称性与守恒量. 由力学体系间的内在联系,时间尺度上Whittaker方程经过力学化,可转化为一般完整系统下的Lagrange方程、相空间Hamilton方程及广义Birkhoff方程,根据Noether理论,建立广义Noether等式,获取守恒量. 最后考虑不同形式的力学函数,计算分析Whittaker方程得到的守恒量.

     

    Abstract: The Noether symmetries and conserved quantities of the Whittaker equation on time scale were studied. With the help of internal connections between various mechanical systems, the Whittacker equation on time scale, after mechanization, is transformed into the Lagrange equation, the Hamilton equation in phase space or the generalized Birkhoff equation in general complete systems. Then, following the Noether theory, a generalized Noether equation was established to find conserved quantities. Finally, the conserved quantities obtained for the Whittacker equations with various mechanical functions are simulated and analyzed.

     

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