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• W2321893749 abstract "The aim of this paper is to provide the state of the art on libration point orbits. We will focus in the Dynamical Systems approach to the problem, since we believe that it provides the most global picture and, at the same time, allows to do the best choice of both strategy and parameters in several mission analysis aspects. I. Dynamics and phase space around the Libration Points 1 Equations of motion and Libration Points 1.1 The Restricted Three Body Problem and its perturbations It is well known that several very simple models, such as the Two Body Problem or the Restricted Three Body Problem (RTBP), are suitable for spacecraft mission design, since they give good insight of the dynamics in many real situations. In this section we will review some of the most relevant restricted models for the analysis of the motion in the vicinity of the libration points. Most of the well known restricted problems take as starting point the circular RTBP, that models the motion of a massless particle under the gravitational attraction of two punctual primaries revolving in circular orbits around their center of mass. In a suitable coordinate system and with adequate units, the Hamiltonian of the RTBP is (Szebehely [70]) H(x, y, z, px, py, pz) = 1 2 (px + p 2 y + p 2 z) + ypx − xpy − 1− μ ((x− μ)2 + y2 + z2)1/2 − μ ((x− μ+ 1)2 + y2 + z2)1/2 , being μ = m2/(m1 + m2), where m1 > m2 are the masses of the primaries. In order to get closer to more realistic situations, or simplifications, this model is modified in different ways. For instance, 1. Hill’s problem. Is useful for the analysis of the motion aroundm2. Can be obtained setting the origin at m2, rescaling coordinates by a factor μ1/3 and keeping only the dominant terms of the expanded Hamiltonian in powers of μ1/3. The Hamiltonian function is H = 1 2 (px + p 2 y + p 2 z) + ypx − xpy − 1 (x2 + y2 + z2)1/2 − x + 1 2 (y + z). This Hamiltonian corresponds to a Kepler problem perturbed by the Coriolis force and the action of the Sun up to zeroth-order in μ1/3. Hill’s model is the first approximation to Departament de Matematica Aplicada i Analisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya, E.T.S.E.I.B., Diagonal 647, 08028 Barcelona, Spain Departament de Matematica Aplicada i Analisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain" @default.
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• W2321893749 date "2003-05-01" @default.
• W2321893749 modified "2023-10-16" @default.
• W2321893749 title "LIBRATION POINT ORBITS: A SURVEY FROM THE DYNAMICAL POINT OF VIEW" @default.
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• W2321893749 doi "https://doi.org/10.1142/9789812704849_0016" @default.
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