Chebyshev Polynomial

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

An orthogonal polynomial system used to approximate the position and velocity of periodic orbits. The paper uses Chebyshev polynomials to express the position and velocity components on the LEO parking orbit and DRO target orbit, serving as constraints for tangential patching between the transfer trajectory and the parking/target orbits.

Application Value

该轨道类型可作为地月空间运输网络的中转站或任务的目标轨道。在设计地月转移方案时，利用该轨道特性可降低任务总速度增量需求。该多项式逼近方法可用于高效表达轨道边界条件。

Related Concepts

• Powered Phase
• Nuclear Electric Propulsion
• Mid-course Correction
• Failure Detection, Isolation, and Recovery

References

• Transfer to Distant Retrograde Orbits Using Manifold Theory
• Gómez et al. 2001, Ch.1