二体问题的探讨  

Discussion on the two-body problem

作　　者：林灏宸 马丽[1] LIN Hao-chen;MA Li(School of Science,Xi’an University of Technology,Xi’an Shaanxi 710048,China)

机构地区：[1]西安理工大学理学院,陕西西安710048

出　　处：《大学物理》2022年第8期71-75,共5页College Physics

摘　　要：二体问题在物理学中非常常见,尤其是在碰撞和天体问题中应用广泛,当多体问题中摄动力远小于二体间相互作用力时,可将其近似看成是二体系统.本文从变换参考系和能量守恒两个角度推导出柯尼希定理,引出折合质量对二体问题进行修正,提出等效一体化的思路来处理问题,简化了二体问题的讨论.此外还引入了退化椭圆求时间的方法,巧妙求解两物体在平方反比作用力下从相对静止到碰撞的时间问题.最后,对二体问题的多解法进行了讨论与改进,用天体系统二体问题的结论类比两个点电荷问题,避免书中积分的繁琐,突出了对问题等效一体化处理的优越性.Two-body problems are very common in physics, especially in collision and celestial body problems. When the perturbation force of the multi-body problem is far less than the interaction force between two bodies, it can be approximated as a two-body system. In this paper, koenig’s theorem is derived from two perspectives of transformation of reference frame and conservation of energy, which leads to the two-body modification of the problem by reduced mass, and puts forward the idea of equivalent integration to deal with the problem, which simplifies the discussion of the two-body problem. At the same time, the degenerate ellipse time method is introduced to solve the time problem from relative rest to collision of two bodies under inverse square force. Finally, we discuss and improve the multi-solution method of the two-body problem, and use the conclusion of the two-body problem of the celestial system to compare the two-body problem with the two-point charge problem, so as to avoid the complicated integration in the book, and highlight the superiority of the equivalent integration treatment of the problem.

关 键 词：二体问题 折合质量 二体修正 等效一体化 

分 类 号：O314[理学—一般力学与力学基础]