Pseudo-Potential Function
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
In the circular restricted three-body problem, the effective potential obtained by combining gravitational potential with centrifugal potential in the rotating frame. In normalized units, U = (x^2 + y^2)/2 + (1-μ)/r_1 + μ/r_2, where r_1 and r_2 are distances from the small body to the two primaries and μ is the mass ratio. The gradient of this function determines the inertial force (gravitational plus centrifugal) on the small body; zero-gradient points are the libration points. The Coriolis force is not included in the pseudo-potential and must be handled separately in the equations of motion.
Application Value
拟势function is analysiscislunar space动力学problem of theoryfoundation, for spacecraftorbitdesign、missionplanning和control策略制定提供数学支撑. 针对拟势function of 深入research有助于理解cislunar space复杂动力学环境, for futuremissiondesign提供theory支撑和工程参考. In 实际mission中, need结合数值simulation和解析method对拟势functionprogressanalysisverify, 确保design方案满足missionconstraint和performance指标.
Related Concepts
- Time-Varying System
- Lipschitz Condition
- Variable-Time Targeting
- Return Corridor
References
- 曹鹏飞 等 - 2017 - 地月L2点Halo轨道支持的登月轨道优化设计