Collinear Singularity

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

Ill-conditioned phenomenon in Lambert problem where velocity vectors become indeterminate and orbital plane cannot be determined when position vectors are collinear.

Application Value

In orbital transfer design, the Lambert problem is the core mathematical tool for solving optimal transfer trajectories between two points. However, when departure and target positions happen to be collinear, standard Lambert solvers fail, with velocity vectors becoming indeterminate. In practical missions, this means such singular configurations must be avoided, which can be achieved by slightly adjusting transfer time or selecting different midcourse points. This phenomenon also reminds orbital designers to check whether input configurations approach collinear singularities when using Lambert tools for transfer trajectory calculation, employing regularization methods or numerical avoidance strategies when necessary.

References

  • Uncertain Lambert Problem
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Contributors: ouyangjiahong, Ou Yang Jiahong