Higher order approximation to the Hill problem dynamics about the libration points

•A higher order, perturbation solution to the Hill problem is computed.•The solution is valid for the dynamics about the libration points.•The analytical solution captures all the relevant periodic orbits. An analytical solution to the Hill problem Hamiltonian expanded about the libration points has...

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Veröffentlicht in:Communications in nonlinear science & numerical simulation Jg. 59; S. 612 - 628
Hauptverfasser: Lara, Martin, Pérez, Iván L., López, Rosario
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 01.06.2018
Elsevier Science Ltd
Schlagworte:
Approximation
Complex variables
Floating point arithmetic
Hill’s problem
Hopf variables
Lagrangian equilibrium points
Libration
Libration points
Nonlinear equations
Orbits
Periodic orbits
Perturbation methods
Perturbation theory
Studies
Perturbation theory
Hill’s problem
Periodic orbits
Libration points
Complex variables
Floating point arithmetic
Hopf variables
ISSN:1007-5704, 1878-7274
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Zusammenfassung:•A higher order, perturbation solution to the Hill problem is computed.•The solution is valid for the dynamics about the libration points.•The analytical solution captures all the relevant periodic orbits. An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture all the relevant periodic orbits originated from the libration points within a reasonable accuracy, the normalization is approached in complex variables. The validity of the solution extends to energy values considerably far away from that of the libration points and, therefore, can be used in the computation of Halo orbits as an alternative to the classical Lindstedt–Poincaré approach. Furthermore, the theory correctly predicts the existence of the two-lane bridge of periodic orbits linking the families of planar and vertical Lyapunov orbits.
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ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2017.12.007