EARTH-MOON TRAJECTORY DESIGN USING LAGRANGE IMPLICIT FUNCTION THEOREM

摘要

Trajectory design for the Earth-Moon flight of a spacecraft is considered in thepresent paper. The optimal control problem associated with the transfer trajectoryis presented, detailing the resulting two point boundary value problem.Application of Lagrange implicit function theorem to nominal solutions obtainedis subsequently detailed. The practical problem of uncertainty associatedwith impulse application is considered and the sensitivities of the optimal programare utilized to estimate the evolution of the associated impulsive uncertainty.The results obtained conclusively demonstrate the nonlinearity of theproblem, in addition to providing a holistic design tool for generation of neighboringoptimal solutions and performing parametric studies.