非中心力场中经典粒子的轨道参数方程与对称性

把非中心力场中经典粒子运动微分方程写成Ermakov方程的形式，得到Ermakov不变量.用改变时间坐标标度的方法得到用能量H和Ermakov不变量表示的轨道参数方程，并研究两守恒量（能量和Ermakov不变量）相应的无限小变换的Noether对称性、Lie对称性和形式不变性.研究结果表明：与两守恒量相应的无限小变换既具有Noether对称性，也具有Lie对称性和形式不变性. 关键词： 非中心力场 轨道参数方程 守恒量 对称性

Parametric orbit equation and symmetries of classical particle in the field of noncentral force

The differential equations of motion of a classical particle in the field of noncentral force are expressed in Ermakov formalism, and the Ermakov invariant is obtained. By rescaling the time, the parametric orbit equations of the classical particle can be expressed in terms of energy H and Ermakov invariant. The Noether symmetry, Lie symmetry and the form invariance of the transformations of two conserved quantities are studied in this paper. The result indicates that the transformations of the two conserved quantities not only possess Noether symmetry but also possess Lie symmetry and form invariance.