单面完整约束系统Tzénoff方程Mei对称性的共形不变性与守恒量
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摘要
研究了单面完整约束系统Tzénoff方程Mei对称性的共形不变性及其守恒量,在给出Mei对称性定义和判据方程的基础上,进一步给出了系统Mei对称性共形不变性的定义和判据方程,并分析了二者的关系.探究了单面完整约束系统Tzénoff方程Mei对称性共形不变性存在守恒量的条件,导出了存在守恒量的结构方程及其守恒量的具体形式.
Conformal invariance and conserved quantity of Mei symmetry for Tzénoff equation in unilateral holonomic constraint system have been studied in the paper.First,the definition and judgment equation of Mei symmetry have been presented.The definition and judgment equation of Mei symmetry conformal invariance have been further explored and the relation between them has been analyzed.The conditions of conserved quantity for Tzénoff equation in unilateral holonomic constraint system have been researched as well.Finally,the condition equation and specific form of conserved quantity have been deduced.
Conformal invariance and conserved quantity of Mei symmetry for Tzénoff equation in unilateral holonomic constraint system have been studied in the paper.First,the definition and judgment equation of Mei symmetry have been presented.The definition and judgment equation of Mei symmetry conformal invariance have been further explored and the relation between them has been analyzed.The conditions of conserved quantity for Tzénoff equation in unilateral holonomic constraint system have been researched as well.Finally,the condition equation and specific form of conserved quantity have been deduced.
引文
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[13]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).ZHANG L X,LIU H Z,XIN X P.Symmetry reductions,exact equations and the conservation laws of the generalized(3+1)dimensional Zakharov-Kuznetsov equation[J].Acta Physica Sinica,2017,66(8):080201(1-7).
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[17]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.WANG T Z,HAN Y L.Conformal Invariance and conserved quantities of non-holonomic dynamical system with relative motion[J].Journal of Jiangnan University:Natural Sciences Edition,2013,12(2):234-238.
[18]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.WANG X M,LI Y C,XIA L L.Conformal Invariance and conserved quantities of Mei symmetry for mechanico-electrical systems[J].Journal of Guizhou University:Natural Sciences Edition,2009,26(6):32-38.
[19]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):5 150-5 154.CHEN X W,ZHAO Y H,LIU C.Conformal invariance and conserved quantity for holonomic mechanical systems with variable mass[J].Acta Physica Sinica,2009,58(8):5 150-5 154.
[20]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.LI Y M.Conformal invariance for nonholonomic mechanical systems with variable mass[J]Journal of Yunnan University:Natural Sciences Edition,2010,32(1):52-57.
[21]ZHENG S W,JIA L Q,YU H S.Mei Symmetry of Tzénoff equations of holonomic system[J].Chinese Physics,2006,15(7):1 399-1 402
[22]ZHENG S W,XIE J F,LI Y M.Mei symmetry and conserved quantity of Tzénoff equations for nonholonomic systems of nonChetaev,s type[J].Communications in Theoretical Physics,2008,49(4):851-854.
[23]ZHENG S W,WANG J B,CHEN X W,et al.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).
[24]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:自然科学版,2011,33(4):412-416.ZHENG S W,CHEN M.A new conserved quantity by Mei symmetry of Tzénoff equation for the non-holonomic systems[J].Journal of Yunnan University:Natural Sciences Edition,2011,33(4):412-416.
[25]郑世旺,王建波,陈向炜,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).ZHENG S W,WANG J B,CHEN X W,et al.Lie symmetry and their conserved quantities of Tzénoff equations for the vair-able mass nonholonomic systems[J].Acta Physica Sinica,2012,61(11):111101(1-5).
[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.ZHENG S W.Conformal invariance and conserved quantity of Mei symmetry for Tzénoff equations in holonomic systems with variable mass[J].Journal of Shangqiu Normal University,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.MEI F X,LIU D,LUO Y.Advanced analytical mechanics[M].Beijing:Beijing Institute of Technology Press,1991.
[2]MEI F X.Form invariance of Lagrange system[J].Journal of Beijing Institute of Technology,2000,9(2):120-124.
[3]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.MEI F X.The symmetry and the conserved quantities of the constraint mechanical system[M].Beijing:Beijing Institute of Technology Press,2004.
[4]FU J L,WANG X J,XIE F P.Conserved quantities and conformal mechanico-electrical systems[J].Chinese Physics Letters,2008,25(7):2 413-2 416.
[5]ZHAO L,FU J L.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).
[6]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.LIU C,ZHAO Y H,CHEN X W.Geometric representation of Noether symmetry for dynamical systems[J].Acta Physica Sinica,2010,59(1):11-14.
[7]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):3 617-3 619.FANG J H.A kind of conserved quantity of Mei symmetry[J].Acta Physica Sinica,2009,58(6):3 617-3 619.
[8]LI Y M.Lie Symmetries,perturbation to symmetries and adiabatic invariants of a generalized birkhoff system[J].Chinese Physics Letters,2010,27(1):010202(1-4).
[9]LUO S K,LI Z J,WANG P,et al.A Lie symmetrical basic integral variable relation and a new conservation law for generalized Hamiltonian systems[J].Acta Mechanica,2013,224(1):71-84.
[10]孙现亭,张美玲,张耀宇,等.变质量相对运动力学系统Nielsen方程的Noether守恒量[J].云南大学学报:自然科学版,2014,36(3):360-365.SUN X T,ZHANG M L,ZHANG Y Y,et al.Noether conserved quantity for Nielsen equations in a variable mass holonomic dynamical system of the relative motion[J].Journal of Yunnan University:Natural Sciences Edition,2014,36(3):360-365.
[11]孔楠,朱建青.时间尺度上Lagrange系统Mei对称其直接导致的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 Mei symmetry of the Lagrange system on time scales[J].Journal of Yunnan University:Natural Sciences Edition,2017,39(2):219-224.
[12]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 a Birkhoffian system in event space[J].Journal of Yunnan University:Natural Sciences Edition,2016,38(3):406-411.
[13]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).ZHANG L X,LIU H Z,XIN X P.Symmetry reductions,exact equations and the conservation laws of the generalized(3+1)dimensional Zakharov-Kuznetsov equation[J].Acta Physica Sinica,2017,66(8):080201(1-7).
[14]ГалиуллинАС,ГафаровГГ,МалайшкаРП,et al.АналитическаяДинамикаСистемГельмгольца,Виркгофа,Намбу:Монография[M].Mockba:РедакцияЖурнала“УспехиФизическихНаук”,1997.
[15]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):5 369-5 373.CAI J L,MEI F X.Conformal invariance and conserved quantity of Lagrange systems[J].Acta Physica Sinica,2008,57(9):5 369-5 373.
[16]刘畅,刘世兴,梅凤翔,等.广义Hamilton系统的共形不变性与Hojman守恒量[J].物理学报,2008,57(11):6 709-6 713.LIU C,LIU S X,MEI F X,et al.Conformal invariance and Hojman conserved quantities[J].Acta Physica Sinica,2008,57(11):6 709-6 713.
[17]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.WANG T Z,HAN Y L.Conformal Invariance and conserved quantities of non-holonomic dynamical system with relative motion[J].Journal of Jiangnan University:Natural Sciences Edition,2013,12(2):234-238.
[18]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.WANG X M,LI Y C,XIA L L.Conformal Invariance and conserved quantities of Mei symmetry for mechanico-electrical systems[J].Journal of Guizhou University:Natural Sciences Edition,2009,26(6):32-38.
[19]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):5 150-5 154.CHEN X W,ZHAO Y H,LIU C.Conformal invariance and conserved quantity for holonomic mechanical systems with variable mass[J].Acta Physica Sinica,2009,58(8):5 150-5 154.
[20]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.LI Y M.Conformal invariance for nonholonomic mechanical systems with variable mass[J]Journal of Yunnan University:Natural Sciences Edition,2010,32(1):52-57.
[21]ZHENG S W,JIA L Q,YU H S.Mei Symmetry of Tzénoff equations of holonomic system[J].Chinese Physics,2006,15(7):1 399-1 402
[22]ZHENG S W,XIE J F,LI Y M.Mei symmetry and conserved quantity of Tzénoff equations for nonholonomic systems of nonChetaev,s type[J].Communications in Theoretical Physics,2008,49(4):851-854.
[23]ZHENG S W,WANG J B,CHEN X W,et al.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).
[24]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:自然科学版,2011,33(4):412-416.ZHENG S W,CHEN M.A new conserved quantity by Mei symmetry of Tzénoff equation for the non-holonomic systems[J].Journal of Yunnan University:Natural Sciences Edition,2011,33(4):412-416.
[25]郑世旺,王建波,陈向炜,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).ZHENG S W,WANG J B,CHEN X W,et al.Lie symmetry and their conserved quantities of Tzénoff equations for the vair-able mass nonholonomic systems[J].Acta Physica Sinica,2012,61(11):111101(1-5).
[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.ZHENG S W.Conformal invariance and conserved quantity of Mei symmetry for Tzénoff equations in holonomic systems with variable mass[J].Journal of Shangqiu Normal University,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.MEI F X,LIU D,LUO Y.Advanced analytical mechanics[M].Beijing:Beijing Institute of Technology Press,1991.
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