Jacobi Field
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
A nontrivial solution of the variational (linearized Hamiltonian) equation along a reference extremal. A Jacobi field is said to be vertical at a time t if its state component vanishes. A positive time tc is conjugate to t=0 if there exists a Jacobi field vertical at both times. Numerically, conjugate times are detected by evaluating the rank of four Jacobi fields, forming the standard algorithm for local optimality verification.
Application Value
A nontrivial solution of the variational (linearized Hamiltonian) equation along a reference extremal. A Jacobi field is said to be vertical at a time t if its state component vanishes. A positive time tc is conjugate to t=0 if there exists a Jacobi field vertical at both times. Numerically, conjugate times are detected by evaluating the rank of four Jacobi fields, forming the standard algorithm for local optimality verification.
Related Concepts
- Time-Varying System
- Lipschitz Condition
- Variable-Time Targeting
- Return Corridor
References
- Caillau et al. 2012 - Minimum fuel control of the planar circular restricted three-body problem