非Chetaev型非完整系统Tzénoff方程Mei对称性的共形不变性与守恒量
|
摘要
研究了非Chetaev型非完整约束系统Tzénoff方程Mei对称性的共形不变性及其守恒量,在给出该系统Mei对称性定义和判据方程的基础上,进一步给出了Mei对称性共形不变性的定义和判据方程.探究了非Chetaev型非完整约束系统Tzénoff方程Mei对称性共形不变性存在守恒量的条件,导出了守恒量存在的条件方程及其守恒量的具体形式.
Conformal invariance and conserved quantity of Mei symmetry for Tzénoff equation in non-Chetaev nonholonomic constraint system are studied in the paper. First,the definition and judgment equation of Mei symmetry are given. The definition and judgment equation of conformal invariance of Mei symmetry are further given. Furthermore,the conditions of conserved quantity for Tzénoff equation in non-Chetaev nonholonomic constraint system are researched. Finally,the condition equation and specific form of conserved quantity are deduced.
Conformal invariance and conserved quantity of Mei symmetry for Tzénoff equation in non-Chetaev nonholonomic constraint system are studied in the paper. First,the definition and judgment equation of Mei symmetry are given. The definition and judgment equation of conformal invariance of Mei symmetry are further given. Furthermore,the conditions of conserved quantity for Tzénoff equation in non-Chetaev nonholonomic constraint system are researched. Finally,the condition equation and specific form of conserved quantity are deduced.
引文
[1]Mei Fengxiang.Form invariance of Lagrange system[J].Journal of Beijing Institute of Technology,2000,9(2):120-124.
[2]梅凤翔.约束力学系统的对称性与守恒量[M].北京:北京理工大学出版社,2004.
[3]Fu Jingli,Wang Xianjun,Xie Fengping.Conserved Quantities and Conformal Mechanico-Electrical Systems[J].Chinese Physics Letters,2008,25(7):2413-2416.
[4]Zhao Li,Fu Jingli.A new type of conserved quantity of Mei symmetry for the motion of mechanico electrical coupling dynamical systems[J].Chinese Physics B,2011,20(4):040201(1-4).
[5]刘畅,赵永红,陈向炜.动力学系统Noether对称性的几何表示[J].物理学报,2010,59(1):11-14.
[6]方建会.Lagrange系统Mei对称性直接导致的一种守恒量[J].物理学报,2009,58(6):3617-3619.
[7]Li Yanmin.Lie Symmetries,Perturbation to Symmetries and Adiabatic Invariants of a Generalized Birkhoff System[J].Chinese Physics Letters,2010,27(1):010202(1-4).
[8]Shao Kai Luo,Zhuang Jun Li,Wang Peng,Lin Li.A Lie symmetrical basic integral variable relation and a new conservation law for generalized Hamiltonian systems[J].Acta Mechanica,2013,224(1):71-84.
[9]李凯辉,刘汉泽,辛祥鹏.一类高阶非线性波方程的李群分析、最优系统、精确解和守恒律[J].物理学报,2016,65(14):140201(1-7).
[10]张丽香,刘汉泽,辛祥鹏.广义(3+1)维Zakharov-Kuznetsov方程的对称约化、精确解和守恒律[J].物理学报,2017,66(8):080201(1-7).
[11]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),2017,39(2):219-224.
[12]ГалиуллинАС,ГафаровГГ,МалайшкаРП,et al.АналитическаяДинамикаСистемГельмгольца,Виркгофа,Намбу:Монография[M].Москва:РедакцияЖурнала“УспехиФизическихНаук”,1997.
[13]蔡建乐,梅凤翔.Lagrange系统Lie点变换下的共形不变性与守恒量[J].物理学报,2008,57(9):5369-5373.
[14]刘畅,刘世兴,梅凤翔,郭永新.广义Hamilton系统的共形不变性与Hojman守恒量[J].物理学报,2008,57(11):6709-6713.
[15]王廷志,韩月林.相对运动非完整动力学系统的共形不变性与守恒量[J].江南大学学报(自然科学版),2013,12(2):234-238.
[16]王小明,李元成,夏丽莉.机电系统Mei对称性的共形不变性与守恒量[J].贵州大学学报(自然科学版),2009,26(6):32-38.
[17]陈向炜,赵永红,刘畅.变质量完整动力学系统的共形不变性与守恒量[J].物理学报,2009,58(8):5150-5154.
[18]李彦敏.变质量非完整力学系统的共形不变性[J].云南大学学报(自然科学版),2010,32(1):52-57.
[19]Zheng Shiwang,Jia Liqun,Yu Hongsheng.Mei Symmetry of Tzénoff Equations of Holonomic System[J].Chinese Physics,2006,15(7):1399-1402.
[20]Zheng Shiwang,Xie Jiafang,Li Yanmin.Mei symmetry and conserved quantity of Tzénoff equations for nonholonomic systems of non-Chetaev,s type[J].Communications in Theoretical Physics,2008,49(4):851-854.
[21]郑世旺,解加芳,陈向炜,等.完整系统Tzénoff方程的Mei对称性直接导致的另一种守恒量[J].物理学报,2010,59(8):5209-5212.
[22]Zheng Shiwang,Wang Jianbo,Chen Xiangwei,Xie Jiafang.Mei symmetry and new conserved quantities of Tzénoff equations for the variable mass higher-order nonholonomic system[J].Chinese Physics Letters,2012,29(2):020201(1-4).
[23]郑世旺,陈梅.非完整系统Tzénoff方程的Mei对称性所对应的一种新守恒量[J].云南大学学报,2011,33(4):412-416.
[24]郑世旺,王建波,陈向炜,李彦敏等.变质量非完整系统Tzénoff方程的Lie对称性与其导出的守恒量[J].物理学报,2012,61(11):111101(1-5).
[25]郑世旺,赵永红.完整系统Tzénoff方程Lie对称性的共形不变性与守恒量[J].商丘师范学院学报,2015,31(6):39-43.
[26]郑世旺.变质量完整系统Tzénoff方程Mei对称性的共形不变性与守恒量[J].商丘师范学院学报,2016,32(12):32-36.
[27]梅凤翔,刘端,罗勇.高等分析力学[M].北京:北京理工大学出版社,1991.
[2]梅凤翔.约束力学系统的对称性与守恒量[M].北京:北京理工大学出版社,2004.
[3]Fu Jingli,Wang Xianjun,Xie Fengping.Conserved Quantities and Conformal Mechanico-Electrical Systems[J].Chinese Physics Letters,2008,25(7):2413-2416.
[4]Zhao Li,Fu Jingli.A new type of conserved quantity of Mei symmetry for the motion of mechanico electrical coupling dynamical systems[J].Chinese Physics B,2011,20(4):040201(1-4).
[5]刘畅,赵永红,陈向炜.动力学系统Noether对称性的几何表示[J].物理学报,2010,59(1):11-14.
[6]方建会.Lagrange系统Mei对称性直接导致的一种守恒量[J].物理学报,2009,58(6):3617-3619.
[7]Li Yanmin.Lie Symmetries,Perturbation to Symmetries and Adiabatic Invariants of a Generalized Birkhoff System[J].Chinese Physics Letters,2010,27(1):010202(1-4).
[8]Shao Kai Luo,Zhuang Jun Li,Wang Peng,Lin Li.A Lie symmetrical basic integral variable relation and a new conservation law for generalized Hamiltonian systems[J].Acta Mechanica,2013,224(1):71-84.
[9]李凯辉,刘汉泽,辛祥鹏.一类高阶非线性波方程的李群分析、最优系统、精确解和守恒律[J].物理学报,2016,65(14):140201(1-7).
[10]张丽香,刘汉泽,辛祥鹏.广义(3+1)维Zakharov-Kuznetsov方程的对称约化、精确解和守恒律[J].物理学报,2017,66(8):080201(1-7).
[11]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),2017,39(2):219-224.
[12]ГалиуллинАС,ГафаровГГ,МалайшкаРП,et al.АналитическаяДинамикаСистемГельмгольца,Виркгофа,Намбу:Монография[M].Москва:РедакцияЖурнала“УспехиФизическихНаук”,1997.
[13]蔡建乐,梅凤翔.Lagrange系统Lie点变换下的共形不变性与守恒量[J].物理学报,2008,57(9):5369-5373.
[14]刘畅,刘世兴,梅凤翔,郭永新.广义Hamilton系统的共形不变性与Hojman守恒量[J].物理学报,2008,57(11):6709-6713.
[15]王廷志,韩月林.相对运动非完整动力学系统的共形不变性与守恒量[J].江南大学学报(自然科学版),2013,12(2):234-238.
[16]王小明,李元成,夏丽莉.机电系统Mei对称性的共形不变性与守恒量[J].贵州大学学报(自然科学版),2009,26(6):32-38.
[17]陈向炜,赵永红,刘畅.变质量完整动力学系统的共形不变性与守恒量[J].物理学报,2009,58(8):5150-5154.
[18]李彦敏.变质量非完整力学系统的共形不变性[J].云南大学学报(自然科学版),2010,32(1):52-57.
[19]Zheng Shiwang,Jia Liqun,Yu Hongsheng.Mei Symmetry of Tzénoff Equations of Holonomic System[J].Chinese Physics,2006,15(7):1399-1402.
[20]Zheng Shiwang,Xie Jiafang,Li Yanmin.Mei symmetry and conserved quantity of Tzénoff equations for nonholonomic systems of non-Chetaev,s type[J].Communications in Theoretical Physics,2008,49(4):851-854.
[21]郑世旺,解加芳,陈向炜,等.完整系统Tzénoff方程的Mei对称性直接导致的另一种守恒量[J].物理学报,2010,59(8):5209-5212.
[22]Zheng Shiwang,Wang Jianbo,Chen Xiangwei,Xie Jiafang.Mei symmetry and new conserved quantities of Tzénoff equations for the variable mass higher-order nonholonomic system[J].Chinese Physics Letters,2012,29(2):020201(1-4).
[23]郑世旺,陈梅.非完整系统Tzénoff方程的Mei对称性所对应的一种新守恒量[J].云南大学学报,2011,33(4):412-416.
[24]郑世旺,王建波,陈向炜,李彦敏等.变质量非完整系统Tzénoff方程的Lie对称性与其导出的守恒量[J].物理学报,2012,61(11):111101(1-5).
[25]郑世旺,赵永红.完整系统Tzénoff方程Lie对称性的共形不变性与守恒量[J].商丘师范学院学报,2015,31(6):39-43.
[26]郑世旺.变质量完整系统Tzénoff方程Mei对称性的共形不变性与守恒量[J].商丘师范学院学报,2016,32(12):32-36.
[27]梅凤翔,刘端,罗勇.高等分析力学[M].北京:北京理工大学出版社,1991.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |