哈密顿Ermakov系统的形式不变性

把形式不变性的方法用于研究哈密顿Ermakov系统，从哈密顿Ermakov系统的形式不变性出发，运用比较系数法得到与形式不变性相应的点对称变换生成元的表达式及势能所满足的偏微分方程.结果表明，在点对称变换下，只有自治的哈密顿Ermakov系统才具有形式不变性. 关键词： 哈密顿Ermakov系统 拉格朗日函数 点对称变换 形式不变性

Form invariance for Hamiltonian Ermakov systems

In this paper, we study the Hamiltonian Ermakov systems using the method of form invariance. In terms of the form invariance of the Hamiltonian Ermakov systems,the generator of point symmetry transformations and the partial differential equations for the potential energy are obtained by comparing the coefficients of all monomials.The result indicates that under the point symmetry transformations,only the autonomous Hamiltonian Ermakov systems possess form invariance.