Lawden's Necessary Conditions

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

Four necessary conditions proposed by Lawden in 1963 for determining fuel-optimality of impulsive transfer orbits: (1) the primer vector and its time derivative are continuous throughout the transfer; (2) the primer vector magnitude does not exceed 1, equaling 1 only at impulse application times; (3) impulse direction aligns with the primer vector; (4) these conditions hold for all interior impulses.

Application Value

Lawden's Necessary Conditions are used in orbital design and trajectory optimization to discretize continuous control problems, solving for optimal control sequences via nonlinear programming. In cislunar space missions, this method can be applied to transfer trajectory design, orbit maintenance, and reentry trajectory planning. It reduces computational complexity, improves convergence speed, and is suitable for onboard autonomous guidance applications.

References

  • Pan Xun et al. - 2017 - Fast Calculation Method for Libration Point Two-Impulse Transfer Trajectories
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Contributors: ouyangjiahong, Ou Yang Jiahong