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Impulse control flight to the invariant manifold near collinear libration point

Vasily Shmyrov, Rufat Aminov, Alexander Shmyrov
We consider the special problem of flight from near-Earth orbit to a neighborhood of first collinear libration point of the Sun-Earth system. For such flight the numerical experiments substantiate the adequacy of the model of Hill’s equations, which is the nonlinear approximation of equations of circular limited three-body problem.
Otherwise, we would be obliged to use the model of limited three-body problem (or its approximation) in conjunction with the model of two-body problem for modeling of motion. During of approach to the neighborhood of libration point (in space of positions), the series of impulse controls are implemented. Controls are built on the basis of equations in variations. The purpose of implementing presented controls is hitting the manifold, where a spacecraft will be as long as possible in the linear case. This manifold is achieved when the special functions of phase variables is equal to zero. All the presented studies are illustrated in detail.
CYBERNETICS AND PHYSICS, Vol. 8, No. 2. 2019, 51–57. https://doi.org/10.35470/2226-4116-2019-8-2-51-57
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