弱非完整系统的积分因子与守恒律
|
摘要
为了进一步研究力学系统的守恒律,将积分因子方法应用于弱非完整系统,建立寻找弱非完整系统守恒律的新方法。首先,由弱非完整系统的Routh方程,给出积分因子的定义;其次,得出系统守恒律存在的必要条件,给出确定积分因子的广义Killing方程;最后,得出弱非完整系统的守恒律以及逆定理,并举例说明结果的应用。结果表明,积分因子方法同样适用于求解弱非完整系统的守恒律。
In order to further study the conservation laws of mechanical systems,we have applied the method of integrating factors to a weakly nonholonomic system,which establishes a new method to find out the conservation laws of the weakly nonholonomic system. Firstly,by using the Routh equations of the weakly nonholonomic system,the definition of integrating factors was given. Secondly,the necessary conditions for the existence of the conservation laws of the system were obtained,and the generalized Killing equations for determining the integrating factors were given. Finally,the conservation law and its inverse for the weakly nonholonomic system were obtained,and the application of the result was illustrated. The results show that the method of integrating factors can be used to study the conservation laws of weakly nonholonomic systems.
In order to further study the conservation laws of mechanical systems,we have applied the method of integrating factors to a weakly nonholonomic system,which establishes a new method to find out the conservation laws of the weakly nonholonomic system. Firstly,by using the Routh equations of the weakly nonholonomic system,the definition of integrating factors was given. Secondly,the necessary conditions for the existence of the conservation laws of the system were obtained,and the generalized Killing equations for determining the integrating factors were given. Finally,the conservation law and its inverse for the weakly nonholonomic system were obtained,and the application of the result was illustrated. The results show that the method of integrating factors can be used to study the conservation laws of weakly nonholonomic systems.
引文
[1]NOETHER A E.Invariante variationsprobleme[J].G觟tt Nachr,1918,KI,II:235-257.
[2]LUTZKY M.Dynamical symmetries and conserved quantities[J].Journal of Physics A:Mathematical General,1979,12(7):973-981.
[3]MEI F X.Form invariance of Lagrange system[J].Journal of Beijing Institute of Technology,2000,9(2):120-124.
[4]DJUKIC D S,SUTELA T.Integrating factors and conservation laws for nonconservative dynamical systems[J].International Journal of Nonlinear Mechanics,1984,19(4):331-339.
[5]QIAO Y F,MENG J,ZHAO S H.Existential theorem of conserved quantities for the dynamics of nonholonomic relativistic systems[J].Chinese Physics,2002,11(9):859-863.
[6]QIAO Y F,ZANG Y L,HAN G C.Integrating factors and conservation theorem for holonomicnonconservative dynamical systems in generalized classical mechanics[J].Chinese Physics,2002,11(10):988-992.
[7]LI R J,QIAO Y F.Integrating factors and conservation theorems for Hamilton’s canonical equations of motion of variable mass nonholonomicnonconservative dynamical systems[J].Chinese Physics,2002,11(8):760-764.
[8]张毅,薛纭.Birkhoff系统的积分因子与守恒律[J].力学季刊,2003,24(2):280-285.
[9]张毅,葛伟宽.用积分因子方法研究非完整约束系统的守恒律[J].物理学报,2003,52(10):2362-2367.
[10]束方平,张毅.用积分因子方法研究广义Birkhoff系统的守恒律[J].华中师范大学学报(自然科学版),2014,48(1):42-45.
[11]蔡琼辉,张毅,朱建青.基于El-Nabulsi分数阶模型的广义Birkhoff系统的积分因子方法[J].华中师范大学学报(自然科学版),2018,52(2):182-206.
[12]葛伟宽.弱非完整系统的近似守恒量[J].物理学报,2009,58(10):6729-6731.
[13]韩月林,王肖肖,张美玲,等.弱非完整系统Mei对称性导致的新型精确和近似守恒量[J].物理学报,2013,62(11):110201(1-6).
[14]严斌,张毅.弱非完整系统的Lagrange对称性与守恒量[J].苏州科技学院学报(自然科学版),2016,33(1):17-22.
[15]梅凤翔.弱非完整系统的运动方程及其近似解[J].北京理工大学学报,1989,9(3):10-17.
[2]LUTZKY M.Dynamical symmetries and conserved quantities[J].Journal of Physics A:Mathematical General,1979,12(7):973-981.
[3]MEI F X.Form invariance of Lagrange system[J].Journal of Beijing Institute of Technology,2000,9(2):120-124.
[4]DJUKIC D S,SUTELA T.Integrating factors and conservation laws for nonconservative dynamical systems[J].International Journal of Nonlinear Mechanics,1984,19(4):331-339.
[5]QIAO Y F,MENG J,ZHAO S H.Existential theorem of conserved quantities for the dynamics of nonholonomic relativistic systems[J].Chinese Physics,2002,11(9):859-863.
[6]QIAO Y F,ZANG Y L,HAN G C.Integrating factors and conservation theorem for holonomicnonconservative dynamical systems in generalized classical mechanics[J].Chinese Physics,2002,11(10):988-992.
[7]LI R J,QIAO Y F.Integrating factors and conservation theorems for Hamilton’s canonical equations of motion of variable mass nonholonomicnonconservative dynamical systems[J].Chinese Physics,2002,11(8):760-764.
[8]张毅,薛纭.Birkhoff系统的积分因子与守恒律[J].力学季刊,2003,24(2):280-285.
[9]张毅,葛伟宽.用积分因子方法研究非完整约束系统的守恒律[J].物理学报,2003,52(10):2362-2367.
[10]束方平,张毅.用积分因子方法研究广义Birkhoff系统的守恒律[J].华中师范大学学报(自然科学版),2014,48(1):42-45.
[11]蔡琼辉,张毅,朱建青.基于El-Nabulsi分数阶模型的广义Birkhoff系统的积分因子方法[J].华中师范大学学报(自然科学版),2018,52(2):182-206.
[12]葛伟宽.弱非完整系统的近似守恒量[J].物理学报,2009,58(10):6729-6731.
[13]韩月林,王肖肖,张美玲,等.弱非完整系统Mei对称性导致的新型精确和近似守恒量[J].物理学报,2013,62(11):110201(1-6).
[14]严斌,张毅.弱非完整系统的Lagrange对称性与守恒量[J].苏州科技学院学报(自然科学版),2016,33(1):17-22.
[15]梅凤翔.弱非完整系统的运动方程及其近似解[J].北京理工大学学报,1989,9(3):10-17.