电荷运动轨迹方程解法的讨论

DISCUSSION ON SOLUTIONS TO CHARGE TRAJECTORY EQUATIONS

文章讨论了在库仑有心力作用下点电荷二维运动轨迹方程的不同解法:比耐方程法、Runge-Lenz矢量法以及速度积分法.比耐方程法是利用比耐公式求解微分方程,得出点电荷的运动轨迹;Runge-Lenz矢量法和速度积分法都是从点电荷的动力学方程出发,利用矢量积分得出一个常矢量,并应用该矢量分析得出点电荷的轨迹方程.3种方法得到的轨迹方程是一致的.计算表明,库仑有心力作用下的点电荷的二维运动轨迹为圆锥曲线,并分析了不同初始条件下圆锥曲线的类型.

We have discussed about various solutions to the two-dimensional charge trajectory equation in the coulomb central force interaction,including the methods of Binet equation,Runge-Lenz vector and velocity integration.Binet equation is to obtain the charge trajectory from Binet equation.For both the Runge-Lenz vector method and the velocity integration method,we start from the equation of motion to get a vector constant and obtain the charge trajectory equation.The three methods can get the same trajectory equation.Calculation indicates that the two-dimensional point charge trajectory under the interaction of coulomb centralforce is conic.Different types of the conic with different initial conditions are also analyzed.