标题： 从一个运动常数出发构建拉格朗日和哈密顿结构 显示英文标题

标题： Construction of Lagrangian and Hamiltonian Structures starting from one Constant of Motion

摘要： 从两个运动的一阶方程出发，构造拉格朗日和哈密顿结构的问题被提出。 这种新方法只需要知道动力系统的一个（与时间无关）运动常量。 构造了哈密顿和拉格朗日结构，然后写出并求解哈密顿-雅可比方程，并显式地给出了该问题的第二个（与时间有关）运动常量。 显示英文摘要

摘要： The problem of the construction of Lagrangian and Hamiltonian structures starting from two first order equations of motion is presented. This new approach requires the knowledge of one (time independent) constant of motion for the dynamical system only. The Hamiltonian and Lagrangian structures are constructed, the Hamilton Jacobi equation is then written and solved and the second (time dependent) constant of the motion for the problem is explicitly exhibited.