Differential Correction Method

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A numerical method that uses the linear approximation of the state transition matrix to iteratively correct initial state deviations so that terminal states gradually satisfy constraint conditions. In the three-body Lambert problem, the differential correction method linearizes the nonlinear two-point boundary value problem, using the state transition matrix to establish the mapping between position deviations and velocity corrections. Equation (11) in the paper is the core differential correction equation.

Application Value

The Differential Correction Method establishes a linear mapping between deviations and corrections using the state transition matrix, serving as the standard method for solving two-point boundary value problems in the three-body Lambert problem. Orbit designers use it to accurately compute libration point rendezvous orbits.

References

  • 基于三体Lambert算法的平动点交会轨道设计
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Contributors: ouyangjiahong, Ou Yang Jiahong