限制性三体问题轨道能量与雅可比常数概念辨析  

DISCUSSION ON ORBITAL ENERGY AND JACOBI CONSTANT IN THE RESTRICTED THREE-BODY PROBLEM

作　　者：齐毅 祁瑞[1] QI Yi;QI Rui(School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]北京理工大学宇航学院,北京100081

出　　处：《力学与实践》2025年第1期216-220,共5页Mechanics in Engineering

基　　金：北京市高等教育学会2022年立项面上课题(MS2022112,MS2022044);北京理工大学2023年一般教改项目(2023CGJG029);聚能课程立项项目资助。

摘　　要：在轨道力学教学中,学生容易将圆型限制性三体问题的航天器轨道能量与雅可比常数混淆。针对该问题,本文推导了轨道能量变化表达式,揭示了轨道能量变化机理,给出了一种新的推导雅可比常数表达式的简便方法,明晰了轨道能量和雅可比常数概念的区别。相关教学研究将帮助学生厘清三体轨道动力学学习难点。In the college classroom teaching of the orbital mechanism,students are easily confused with Jacobi constant of the circular restricted three-body problem with the orbital energy of the spacecraft.To solve this issue,in this paper,we derive the expression of the derivation of orbital energy,and uncover the mechanism of the gravity assist or flyby.Then,a new and concise approach to derive Jacobi constant is proposed.Finally,the difference between the orbital energy and Jacobi constant is clarified.The result in this paper can help students figure out the key point in the orbital dynamics.

关 键 词：限制性三体问题 轨道能量 雅可比常数 

分 类 号：O313.1[理学—一般力学与力学基础]