Jacobi Constant

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

The sole conserved quantity (integral of motion) in the CR3BP, defined as JC = 2U - ẋ² - ẏ² - ż². It combines the pseudo-potential and velocity components, playing a role analogous to energy conservation. Orbits sharing the same JC value reside at the same energy level, enabling transfers between them that require only geometry changes rather than energy changes.

Application Value

This concept has important application value in cislunar space research and mission design.

Related Concepts

• Nonlinear Programming
• Zero-Velocity Curve
• Shape-Based Method

References

• DOI:10.16804/j.cnki.issn1006-3242.2023.05.009
• Zimovan-Spreen et al. 2022
• /home/ouyangjiahong/Downloads/地月空间相关/output/Fu 等 - 2022 - Stochastic optimization for stationkeeping of periodic orbits using a high-order target point approa/hybrid_auto/Fu 等 - 2022 - Stochastic optimization for stationkeeping of periodic orbits using a high-order target point approa.md
• Chao 等 - 2022
• Clustering natural trajectories in the Earth-moon circular restricted three-body problem
• Gómez 等 - 2001
• Parker和Anderson - 2014 - Low-energy lunar trajectory design
• Szebehely - 1967 - Theory of orbit the restricted problem of three bodies