Strengthened Legendre-Clebsch Condition

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A second-order necessary condition in optimal control theory used to determine the correct sign of optimal control variables. It requires the second partial derivative of the Hamiltonian with respect to control to be strictly positive, ensuring the control law yields a local minimum rather than maximum. Used in the paper to determine the signs of thrust direction cosines.

Application Value

This term has application value in the design and analysis of cislunar space missions, supporting trajectory design, mission planning, and system optimization. Researchers can analyze its physical mechanisms and engineering applicability based on specific mission requirements to advance cislunar space exploration technology.

References

  • Kluever and Pierson, 1995
Improve this page
Last Updated:
Contributors: ouyangjiahong, Ou Yang Jiahong