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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| Published in: | Communications in nonlinear science & numerical simulation Vol. 59; pp. 612 - 628 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Amsterdam
Elsevier B.V
01.06.2018
Elsevier Science Ltd |
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| ISSN: | 1007-5704, 1878-7274 |
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| Abstract | •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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| AbstractList | 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. •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. |
| Author | Pérez, Iván L. López, Rosario Lara, Martin |
| Author_xml | – sequence: 1 givenname: Martin surname: Lara fullname: Lara, Martin email: mlara0@gmail.com organization: ETSI Aeronáuticos, Plaza del Cardenal Cisneros 3, Madrid 28040, Spain – sequence: 2 givenname: Iván L. surname: Pérez fullname: Pérez, Iván L. email: ivan.perez@unirioja.es organization: Scientific Computing Group (GRUCACI), University of La Rioja, San José de Calasanz 31, 26004 Logroño, Spain – sequence: 3 givenname: Rosario surname: López fullname: López, Rosario email: rlgomez@riojasalud.es organization: Scientific Computing Group (GRUCACI), Center for Biomedical Research of La Rioja, Piqueras 98, 26006 Logroño, Spain |
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| Keywords | Perturbation theory Hill’s problem Periodic orbits Libration points Complex variables Floating point arithmetic Hopf variables |
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| Snippet | •A higher order, perturbation solution to the Hill problem is computed.•The solution is valid for the dynamics about the libration points.•The analytical... An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to... |
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| SubjectTerms | 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 |
| Title | Higher order approximation to the Hill problem dynamics about the libration points |
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