从第一积分求Lagrange函数和等效的Lagrange函数

From First Integral to Construct Lagrangian and Equivalent Lagrangians

讨论了直接从运动方程第一积分构造Lagrange函数的新方法和等效的Lagrange函数之间的关系,得到了一类同位等效Lagrange函数族存在的判据和直接构造法.应用所得结果构造了若干系统的Lagrange函数和函数族.

The relations between the approach to construction of Lagrangian from the integral of motion equations and the equivalent Lagrangians are discussed. The existence criterion and the direct construction methods for a family of the isotropic equivalent Lagrangians are obtained. By use of the results, the Lagrangians and families of Lagrangians for some systems are constructed.