Calculus of Variations

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A branch of mathematics dealing with extremal problems of functionals, forming the theoretical basis for optimal control. Euler-Lagrange equations and necessary conditions can be derived through calculus of variations.

Application Value

Calculus of Variations plays an important role in orbital dynamics and attitude control, serving as a critical tool for analyzing spacecraft motion characteristics. Research on this concept enables optimization of orbit transfer schemes and improvement of control system performance.

Related Concepts

• Restricted Three-Body Problem
• KAM Theorem
• Hill Clohessy Wiltshire Equations
• State Transition Function

References

• Conway - 2010 - Spacecraft trajectory optimization.