时间尺度上相空间中力学系统的Mei对称性及守恒量
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摘要
研究时间尺度上相空间中力学系统的Mei对称性及守恒量。首先,根据时间尺度上Lagrange方程推导出了时间尺度上相空间中力学系统的运动微分方程;而后,给出了该系统的Mei对称性的定义和确定方程,同时得到时间尺度上相空间中力学系统Mei对称性的结构方程及守恒量;最后,举例说明结果的应用。
We have studied the Mei symmetry and the conserved quantity in phase space on time scales. First,the dynamic differential equation in phase space on time scales was established based on the Lagrange equations on time scales. Then, the definition and criterion of Mei symmetry in phase space on time scales were given. We obtained the structure equation of Mei symmetry and the conserved quantity. Finally,an example was presented to illustrate the application of the results.
We have studied the Mei symmetry and the conserved quantity in phase space on time scales. First,the dynamic differential equation in phase space on time scales was established based on the Lagrange equations on time scales. Then, the definition and criterion of Mei symmetry in phase space on time scales were given. We obtained the structure equation of Mei symmetry and the conserved quantity. Finally,an example was presented to illustrate the application of the results.
引文
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[3] AGARWAL R,BOHNER M,O′REGAN D. Dynamic equations on time scales:a survey[J]. Journal of Computational and Applied Mathematics,2002,141(1/2):1-26.
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[7] TORRES D F M. The second Euler-Lagrange equation of variational calculus on time scales[J]. European Journal of Control,2011,17(1):9-18.
[8]蔡平平.时间坐标上约束力学系统的对称性理论研究[D].杭州:浙江理工大学,2013.
[9]张毅.时间尺度上Hamilton系统的Noether理论[J].力学季刊,2016,37(2):214-224.
[10]祖启航,朱建青,宋传静.时间尺度上相空间中非chetaev型非完整系统的Noether理论[J].华中师范大学学报(自然科学版),2017,51(1):23-27.
[11]施玉飞,张毅.时间尺度上事件空间中Birkhoff系统的Noether定理[J].苏州科技大学学报(自然科学版),2017,34(3):1-7.
[12] MEI F X. Form invariance of Lagrange system[J]. Journal of Beijing Institute of Technology,2000,9(2):120-124.
[13]方建会,廖永潘,彭勇.相空间力学系统的两类Mei对称性及守恒量[J].物理学报,2005,54(2):500-503.
[14]方建会,王鹏,丁宁.相空间中力学系统的Lie-Mei对称性[J].物理学报,2006,55(8):3821-3824.
[15]张毅.相空间单面完整约束力学系统的对称性与守恒量[J].物理学报,2005,54(10):4488-4495.
[16]张毅,尚玫.相空间中非完整力学系统的对称性与非Noether守恒量[J].苏州科技学院学报(自然科学版),2007,24(1):1-8.
[17]张毅.相空间非保守系统的Herglotz广义变分原理及其Noether定理[J].力学学报,2016,48(6):1382-1389.
[18]路凯,方建会.相空间中离散完整系统的Noether对称性和Mei对称性[J].物理学报,2009,58(11):7421-7425.
[19]张晔,张毅,陈向炜.事件空间中Birkhoff系统的Mei对称性与守恒量[J].云南大学学报(自然科学版),2016,38(3):406-411.
[20]孔楠,朱建青.时间尺度上Lagrange系统Mei对称性及其导致的Mei守恒量[J].云南大学学报(自然科学版),2017,39(2):219-224.
[21]党卫华,梁景辉.准坐标下完整力学系统Mei对称性的共形不变性与守恒量[J].江西科学,2013,31(4):433-438.
[22]黄卫立.一般完整系统Mei对称性的逆问题[J].物理学报,2015,64(17):9-14.
[23]宋静,张毅.基于非标准Lagrange函数和动力学系统的Noether-Mei对称性与守恒量[J].中山大学学报(自然科学版),2017,56(3):26-30.
[24]王雪萍,张毅. Birkhoff系统的Noether-Mei对称性与守恒量[J].中山大学学报(自然科学版),2016,55(4):53-55.
[25]王菲菲,方建会.离散变质量完整系统的Noether对称性与Mei对称性[J].物理学报,2014(17):12-17.
[2] BOHNER M,PETERSON A. Dynamic Equations on Time Scales:An Introduction with Applications[M]. Boston:Birkh覿user,2001.
[3] AGARWAL R,BOHNER M,O′REGAN D. Dynamic equations on time scales:a survey[J]. Journal of Computational and Applied Mathematics,2002,141(1/2):1-26.
[4] BOHNER M,HUDSON T. Euler-type boundary value problems in quantum calculcs[J]. International Journal of Applied Mathematics&Statistics,2007,9(J07):19-23.
[5] BOHNER M. Calculus of variations on time scales[J]. Dynamic Systems and Applications,2004,13(12):339-349.
[6] TORRES D F M. Noether’s theorem on time scales[J]. Journal of Mathematical Analysis&Applications,2008,342(2):1220-1226.
[7] TORRES D F M. The second Euler-Lagrange equation of variational calculus on time scales[J]. European Journal of Control,2011,17(1):9-18.
[8]蔡平平.时间坐标上约束力学系统的对称性理论研究[D].杭州:浙江理工大学,2013.
[9]张毅.时间尺度上Hamilton系统的Noether理论[J].力学季刊,2016,37(2):214-224.
[10]祖启航,朱建青,宋传静.时间尺度上相空间中非chetaev型非完整系统的Noether理论[J].华中师范大学学报(自然科学版),2017,51(1):23-27.
[11]施玉飞,张毅.时间尺度上事件空间中Birkhoff系统的Noether定理[J].苏州科技大学学报(自然科学版),2017,34(3):1-7.
[12] MEI F X. Form invariance of Lagrange system[J]. Journal of Beijing Institute of Technology,2000,9(2):120-124.
[13]方建会,廖永潘,彭勇.相空间力学系统的两类Mei对称性及守恒量[J].物理学报,2005,54(2):500-503.
[14]方建会,王鹏,丁宁.相空间中力学系统的Lie-Mei对称性[J].物理学报,2006,55(8):3821-3824.
[15]张毅.相空间单面完整约束力学系统的对称性与守恒量[J].物理学报,2005,54(10):4488-4495.
[16]张毅,尚玫.相空间中非完整力学系统的对称性与非Noether守恒量[J].苏州科技学院学报(自然科学版),2007,24(1):1-8.
[17]张毅.相空间非保守系统的Herglotz广义变分原理及其Noether定理[J].力学学报,2016,48(6):1382-1389.
[18]路凯,方建会.相空间中离散完整系统的Noether对称性和Mei对称性[J].物理学报,2009,58(11):7421-7425.
[19]张晔,张毅,陈向炜.事件空间中Birkhoff系统的Mei对称性与守恒量[J].云南大学学报(自然科学版),2016,38(3):406-411.
[20]孔楠,朱建青.时间尺度上Lagrange系统Mei对称性及其导致的Mei守恒量[J].云南大学学报(自然科学版),2017,39(2):219-224.
[21]党卫华,梁景辉.准坐标下完整力学系统Mei对称性的共形不变性与守恒量[J].江西科学,2013,31(4):433-438.
[22]黄卫立.一般完整系统Mei对称性的逆问题[J].物理学报,2015,64(17):9-14.
[23]宋静,张毅.基于非标准Lagrange函数和动力学系统的Noether-Mei对称性与守恒量[J].中山大学学报(自然科学版),2017,56(3):26-30.
[24]王雪萍,张毅. Birkhoff系统的Noether-Mei对称性与守恒量[J].中山大学学报(自然科学版),2016,55(4):53-55.
[25]王菲菲,方建会.离散变质量完整系统的Noether对称性与Mei对称性[J].物理学报,2014(17):12-17.