EARTH-MOON TRAJECTORY DESIGN USING LAGRANGE IMPLICIT FUNCTION THEOREM Conference Paper

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

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