从第一积分求Lagrange函数和等效的Lagrange函数

摘要

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.%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.