Jacobi Constant-Velocity Increment Relationship
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
The analytical relationship between the Jacobi constant C and velocity increment: delta_C = -2v*delta_v. This relationship yields three insights: first, the Jacobi constant and velocity increment have opposite signs, so increasing C (lowering energy) requires deceleration; second, maneuvers at higher speed produce larger changes in C for the same delta_v; third, the velocity increment should be collinear with the velocity direction to maximize energy change efficiency. This relationship provides the theoretical foundation for the four-impulse transfer design method.
Application Value
The analytical relationship between the Jacobi constant C and velocity increment: delta_C = -2v*delta_v. This relationship yields three insights: first, the Jacobi constant and velocity increment have opposite signs, so increasing C (lowering energy) requires deceleration; second, maneuvers at higher speed produce larger changes in C for the same delta_v; third, the velocity increment should be collinear with the velocity direction to maximize energy change efficiency. This relationship provides the theoretical foundation for the four-impulse transfer design method.
Related Concepts
- Bivariate Gaussian Distribution
- Midcourse Impulse
- Zero-Thrust Reference Trajectory
- Co-state Variables
References
- 乔琛远和杨乐平 - 2024 - 地月L1点低能转移轨道设计与优化