Turning Point
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
A point on a homotopy path where the derivative of the parameter with respect to arc length vanishes. At a turning point, the parameter's first derivative with respect to arc length is zero, typically corresponding to a critical state where the extremal loses global optimality (homotopy branch switch) or local optimality (conjugate time appears).
Application Value
This concept has practical applications in cislunar space science and engineering. Related research supports the planning, implementation, and operations of cislunar missions, forming an integral part of the knowledge system in this field.
Related Concepts
- Multiple Segment Trajectory Design
- Zero-Velocity Surface
- Null Vector
- Circular Restricted Three-Body Problem
References
- Caillau and Daoud 2012, SIAM J. Control Optim. 50(6)