Continuation Method
Author: Tianjiang Says
Website: https://cislunarspace.cn
Definition
The continuation method (parameter continuation) is a numerical technique for computing families of orbits by gradually varying a parameter (such as Jacobi constant, orbital amplitude, or period) and using each converged solution as the initial guess for the next computation. It is the primary tool for systematically exploring the orbit design space.
Process
- Start with a known orbit solution (e.g., a converged periodic orbit)
- Perturb the parameter slightly (e.g., increase the Jacobi constant by a small amount)
- Compute a new orbit using differential correction with the previous solution as initial guess
- Store the converged solution
- Repeat until the desired parameter range is covered or a bifurcation is detected
Types
| Type | Description |
|---|---|
| Natural continuation | Vary one parameter along an orbit family |
| Pseudo-arclength continuation | Parameterize by arc length along the solution curve, allowing turning points |
| Branch switching | At bifurcation points, switch to a different orbit family |
Applications
Continuation methods are essential for:
- Orbit family mapping: Computing DRO, Halo, Lissajous, and Lyapunov orbit families
- Bifurcation analysis: Identifying where orbit families branch or terminate
- Design space exploration: Systematically surveying available orbits for mission design
- Stability characterization: Tracking how stability indices change along an orbit family
Related Concepts
References
- Chen Yuju. DRO Orbit Design and Control Research for Cislunar Space Situation Awareness[D]. 2024.