Gauss-Legendre Collocation Method

Author: Tianjiang Shuo Website: https://cislunarspace.cn

Definition

A discretization method for numerically solving differential equations. It uses Legendre polynomial roots (LG points) as collocation points, approximates the solution function with Lagrange interpolation polynomials, and enforces the differential equation at each collocation point, converting the continuous problem into a finite-dimensional algebraic system. This is the core discretization technique of the Gauss pseudospectral method.

Application Value

This concept plays a key role in trajectory transfer design, helping evaluate transfer costs and flight time to provide quantitative basis for mission trade studies. Combined with global search algorithms, multiple solution families and Pareto frontiers can be identified to guide orbital design decisions.

References

  • 平动点周期轨道间小推力转移的Gauss伪谱法
Improve this page
Last Updated:
Contributors: ouyangjiahong, Ou Yang Jiahong