Fixed-Point Homotopy

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A homotopy function construction method. Sets the initial homotopy problem as G(y) = y - y₀, where y₀ is a known initial guess. The homotopy function is H(y, κ) = κF(y) + (1-κ)(y - y₀). When κ = 0, the solution is exactly y₀; as κ increases, it approaches the original problem. Does not depend on the specific form of the original problem, making it broadly applicable.

Application Value

This concept is essential for understanding motion characteristics in orbital design and control, and plays a vital role in mission success.

Related Concepts

• Minimum Norm Solution
• Rigid Body Dynamics
• Variable-Size Design Space, VSDS
• Analytical Gradient

References

• 潘迅和泮斌峰 - 2019 - 基于同伦方法的地月系L2点小推力转移轨道优化