有心力场中质点轨道方程求解问题的讨论

Discuss about Solving of Orbit Equation of Particle in Central Force Field

该文介绍了用正则方程求解受平方反比引力作用的质点轨道方程的方法,推导了质点的角动量守恒定律(mh=恒量)和机械能守恒定律(E=恒量)及其轨道方程。以往用比耐公式求解质点的轨道方程,通常没有给出积分常数的具体形式。该文用E和h确定了用比耐公式法求解的积分常数。这样用比耐公式方法与用机械能守恒方法求解的轨道方程形成了统一的形式,有利于学生更深入地理解受平方反比引力作用质点运动的物理内涵。

This paper has introduced a method with the canonical equations to solve the central force problem ,derived the Law of conservation of angular momentum （mh=constant） and the Law of conservation of machinery energy （E=constant） and the orbit equation of the particle .Existing methods solving of the orbit equation with Binet equation usually do not provide a specific form of integral constants .UsedEandh ,we have determined the integral constant .So ,the orbit equation solved by methods of the Law of conservation and the Binet equation has a unified form .It is useful for students understanding of the physical meaning of particle motion in a central force field .