相对运动动力学Chetaev型非完整系统Appell方程Mei对称性共形不变性和守恒量

Conformal invariance and conserved quantity of Mei symmetry of Appell equations for nonholonomic systems with Chetaevs type in dynamics of relative motion

摘要: 在相对运动动力学Chetaev型非完整系统Appell方程Mei对称性的基础上,进一步研究它的共形不变性及其相应的Mei守恒量.利用引入无限小变换群及其生成元向量,定义该系统Appell方程Mei对称性和Mei对称性的共形不变性,推导出该系统具有Mei对称性和Mei对称性共形不变性的充分与必要条件,得到该系统相应的Mei守恒量.最后,举例说明其应用.

Abstract: On the basis of Mei symmetry of Appell equations for nonholonomic systems with Chetaevs type in dynamics of relative motion,its conformal invariance and relative Mei conserved quantity are further studied.By introducing the infinitesimal transformations of groups and their generating vectors,the definitions of Mei symmetry and conformal invariance of Mei symmetry of Appell equations in the system are given.Necessary and sufficient conditions of which the system has both Mei symmetry and conformal invariance of Mei symmetry,and Mei-conserved quantity deduced directly from Mei symmetry in the system are gained.An example is given to illustrate its application.