时间尺度上Hamilton系统的Mei对称性及守恒量
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摘要
研究了时间尺度上Hamilton系统的Mei对称性及守恒量.给出系统的Mei对称性的定义及判据方程,得到时间尺度上Hamilton系统Mei对称性的结构方程和守恒量的表达式.并举例说明结果的应用.
The Mei symmetry for Hamiltonian system on time scales has been studied in this paper and the definition and criterion of Mei symmetry have been explored.Meanwhile,the expressions of the structural equation and conserved quantity of Mei symmetry for Hamiltonian system on time scales have been obtained. Finally,we have presented an example to illustrate the application of the theorem.
The Mei symmetry for Hamiltonian system on time scales has been studied in this paper and the definition and criterion of Mei symmetry have been explored.Meanwhile,the expressions of the structural equation and conserved quantity of Mei symmetry for Hamiltonian system on time scales have been obtained. Finally,we have presented an example to illustrate the application of the theorem.
引文
[1]HILGER S.Ein mabkettenkalkul mit anwendung auf zenrtumsmannig faltigkeiten[D].Wurzburg:University Wurzburg,1988.
[2]HILGER S.Analysis on measure chains-a unified approach to continuous and discrete calculus[J].Results Math,1990,18(1):18-56.
[3]HILGER S.Differential and difference calculus-unified[J].Nonlinear Anal,1997,30(5):2 683-2 694.
[4]BOHNER M,PETERSON A.Advances in dynamic equations on time scales[M].Boston:Birkhuser,2003.
[5]AGARWAL R,BOHNER M,O'REGAN D,et al.Dynamic equations on time scales:a survey[J].Journal of Computational and Applied Mathematics,2002,141(1/2):1-26.
[6]BOHNER M,HUDSON T.Euler-type boundary value problems in quantum calculcs[J].International Journal of Applied Mathematics&Statistics,2007,9(J07):19-23.
[7]MEI F X.Form invariance of lagrange system[J].Journal of Beijing Institute of Technology,2000,9(2):120-124.
[8]贾立群,张耀宇,郑世旺.Chetaev型约束力学系统Appell方程的Mei对称性与Mei守恒量[J].云南大学学报:自然科学版,2007,29(6):589-595.JIA L Q,ZHANG Y Y,ZHENG S W.Mei symmetry and Mei conserved quantity for Appell equation in Chetaev constraint mechanical systems[J].Journal of Yunnan University:Natural Sciences Edition,2007,29(6):589-595..
[9]刘仰魁.一般完整力学系统Mei对称性的一种守恒量[J].物理学报,2010,59(1):7-10.LIU Y K.A conserved quantity for Mei symmetry of general complete mechanical system[J].Journal of Physics,2010,59(1):7-10.
[10]杨新芳,贾立群.三大力学体系的Mei对称性导致的Mei守恒量[D].无锡:江南大学,2010.YANG X F,JIA L Q.Mei conserved quantity of Mei symmetry for the three mechanical systems[D].Wuxi:Jiangnan University,2010.
[11]罗绍凯.Hamilton系统的Mei对称性、Noether对称性和Lie对称性[J].物理学报,2003,52(12):2 941-2 944.LUO S K.Mei symmetry,Noether symmetry and Lie symmetry of Hamiltonian system[J].Acta Phys Sin,2003,52(12):2 941-2 944.
[12]姜文安,罗绍凯.广义Hamilton系统的Mei对称性导致的Mei守恒量[J].物理学报,2011,60(6):1-5.JIANG W A,LUO S K.Mei symmetry leading to Mei conserved quantity of generalized hamiltonnian system[J].Acta Phys Sin,2011,60(6):1-5.
[13]吴惠斌,许学军.完整系统形式不变性导致的新守恒量[J].北京理工大学学报,2004,24(6):469-471.WU H B,XU X J.New conserved quantity for the form invariance of complete system[J].Journal of Beijing Institute of Technology,2004,24(6):469-471.
[14]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.ZHANG Y,ZHANG Y,CHEN X W.Mei symmetry and conserved quantity of Birkhoff system in event space[J].Journal of Yunnan University:Natural Sciences Edition,2016,38(3):406-411.
[15]TORRES D F M.Noether’s theorem on time scales[J].J Math Appl,2008,342(2):1 220-1 226.
[16]张毅.时间尺度上Hamilton系统的Noether理论[J].力学季刊,2016,37(2):214-224.ZHANG Y.Noether theory for Hamiltonian system on time scales[J].Chinese Quarterly of Mechanics,2016,37(2):214-224.
[17]CAI P P,FU J L,GUO Y X.Noether symmetries of the nonconservative and nonholonomic system on time scales[J].Sci China:Phys Mech Astron,2013,56(5):1 017-1 028.
[18]PENG K K,LUO Y P.Dynamics symmetries of Hamiltonian system on time scales[J].Journal of Mathematical Physics,2014,55(4):2 683-2 694.
[19]孔楠,朱建青.时间尺度上Lagrange系统Mei对称性及其直接导致的Mei守恒量[J].云南大学学报:自然科学版,2017,39(2):219-224.KONG N,ZHU J Q.On the Mei conserved quantity caused directly by the Mei symmetry of the Lagrange system on time scales[J].Journal of Yunnan University:Natural Sciences Edition,2017,39(2):219-224.
[20]BOHNER M.Calculus of variations on time scales[J].Dynam Syst Appl,2004,13(12):339-349.
[21]BOHNER M,GEORGIEV S Q.Partial differentiation on time scales[J].Dynamic Systems and Applications,2016,13(3):351-379.
[22]MARTIN BOHNER,ALLAN PETERSON.Dynamic equations on time scales[M].New York:Springer Science Business Media,2001.
[2]HILGER S.Analysis on measure chains-a unified approach to continuous and discrete calculus[J].Results Math,1990,18(1):18-56.
[3]HILGER S.Differential and difference calculus-unified[J].Nonlinear Anal,1997,30(5):2 683-2 694.
[4]BOHNER M,PETERSON A.Advances in dynamic equations on time scales[M].Boston:Birkhuser,2003.
[5]AGARWAL R,BOHNER M,O'REGAN D,et al.Dynamic equations on time scales:a survey[J].Journal of Computational and Applied Mathematics,2002,141(1/2):1-26.
[6]BOHNER M,HUDSON T.Euler-type boundary value problems in quantum calculcs[J].International Journal of Applied Mathematics&Statistics,2007,9(J07):19-23.
[7]MEI F X.Form invariance of lagrange system[J].Journal of Beijing Institute of Technology,2000,9(2):120-124.
[8]贾立群,张耀宇,郑世旺.Chetaev型约束力学系统Appell方程的Mei对称性与Mei守恒量[J].云南大学学报:自然科学版,2007,29(6):589-595.JIA L Q,ZHANG Y Y,ZHENG S W.Mei symmetry and Mei conserved quantity for Appell equation in Chetaev constraint mechanical systems[J].Journal of Yunnan University:Natural Sciences Edition,2007,29(6):589-595..
[9]刘仰魁.一般完整力学系统Mei对称性的一种守恒量[J].物理学报,2010,59(1):7-10.LIU Y K.A conserved quantity for Mei symmetry of general complete mechanical system[J].Journal of Physics,2010,59(1):7-10.
[10]杨新芳,贾立群.三大力学体系的Mei对称性导致的Mei守恒量[D].无锡:江南大学,2010.YANG X F,JIA L Q.Mei conserved quantity of Mei symmetry for the three mechanical systems[D].Wuxi:Jiangnan University,2010.
[11]罗绍凯.Hamilton系统的Mei对称性、Noether对称性和Lie对称性[J].物理学报,2003,52(12):2 941-2 944.LUO S K.Mei symmetry,Noether symmetry and Lie symmetry of Hamiltonian system[J].Acta Phys Sin,2003,52(12):2 941-2 944.
[12]姜文安,罗绍凯.广义Hamilton系统的Mei对称性导致的Mei守恒量[J].物理学报,2011,60(6):1-5.JIANG W A,LUO S K.Mei symmetry leading to Mei conserved quantity of generalized hamiltonnian system[J].Acta Phys Sin,2011,60(6):1-5.
[13]吴惠斌,许学军.完整系统形式不变性导致的新守恒量[J].北京理工大学学报,2004,24(6):469-471.WU H B,XU X J.New conserved quantity for the form invariance of complete system[J].Journal of Beijing Institute of Technology,2004,24(6):469-471.
[14]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.ZHANG Y,ZHANG Y,CHEN X W.Mei symmetry and conserved quantity of Birkhoff system in event space[J].Journal of Yunnan University:Natural Sciences Edition,2016,38(3):406-411.
[15]TORRES D F M.Noether’s theorem on time scales[J].J Math Appl,2008,342(2):1 220-1 226.
[16]张毅.时间尺度上Hamilton系统的Noether理论[J].力学季刊,2016,37(2):214-224.ZHANG Y.Noether theory for Hamiltonian system on time scales[J].Chinese Quarterly of Mechanics,2016,37(2):214-224.
[17]CAI P P,FU J L,GUO Y X.Noether symmetries of the nonconservative and nonholonomic system on time scales[J].Sci China:Phys Mech Astron,2013,56(5):1 017-1 028.
[18]PENG K K,LUO Y P.Dynamics symmetries of Hamiltonian system on time scales[J].Journal of Mathematical Physics,2014,55(4):2 683-2 694.
[19]孔楠,朱建青.时间尺度上Lagrange系统Mei对称性及其直接导致的Mei守恒量[J].云南大学学报:自然科学版,2017,39(2):219-224.KONG N,ZHU J Q.On the Mei conserved quantity caused directly by the Mei symmetry of the Lagrange system on time scales[J].Journal of Yunnan University:Natural Sciences Edition,2017,39(2):219-224.
[20]BOHNER M.Calculus of variations on time scales[J].Dynam Syst Appl,2004,13(12):339-349.
[21]BOHNER M,GEORGIEV S Q.Partial differentiation on time scales[J].Dynamic Systems and Applications,2016,13(3):351-379.
[22]MARTIN BOHNER,ALLAN PETERSON.Dynamic equations on time scales[M].New York:Springer Science Business Media,2001.