拉格朗日函数在平面摆运动中的应用

The Application of Lagrangian Function in the Motion of Plane Pendulum

通过拉格朗日函数求解系统的运动方程是近代物理的一个重要分析方法。本文以平面摆为例,通过建立系统的拉格朗日函数,得到系统的广义动量,并确定系统的能量、轨迹与振动周期的精确表达式,其极限条件下的周期与小角度单摆一致。

Through the Lagrange function for solving system equations of motion is an important analysis method of modern physics.In this paper,we take plane pendulum for example.By establishing the lagrangian function of system,we get the generalized momentum,the total energy,trajectory and oscillation period of system,in the limit situation the period tend to in accordance with simple pendulum at small angle.