Schubart Solutions in the Charged Collinear Three-Body Problem

Ortega, Alberto Castro; Falconi, Manuel

doi:10.1007/s10884-015-9451-0

Cited by 5 publications

(1 citation statement)

References 13 publications

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“…Some earlier work on the periodic orbits can be referred to Hadjidemetriou (1984). Three classical families of periodic orbits of the three-body problem are of Euler-Lagrange type (Meyer and Schmidt 1986;Sicardy 2010;Hu and Sun 2010;Zhou and Long 2017), figure-eight type (Chenciner and Montgomery 2000;Muñoz-Almaraz et al 2007;Chen and Lin 2009;Hu and Sun 2009;Galan-Vioque et al 2014;Yu 2017) and "Broucke-Hénon","Schubart-like" type (Hénon 1974(Hénon , 1976Martínez 2013;Ortega and Falconi 2016;Voyatzis et al 2018;Kuang et al 2019). It is summarized in that only these three families and a few more new periodic orbits are numerically calculated before a series of their work, and more than 2000 families of periodic orbits are found by taking use of the "clean numerical simulation" (CNS) technique, the grid search and the Newton-Raphson method on a supercomputer.…”

Section: Introductionmentioning

confidence: 99%

Determination of the doubly symmetric periodic orbits in the restricted three-body problem and Hill’s lunar problem

2023

Celest Mech Dyn Astron

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We review some recent progress on the research of the periodic orbits of the N-body problem, and numerically study the spatial doubly symmetric periodic orbits (SDSPs for short). Both comet- and lunar-type SDSPs in the circular restricted three-body problem are computed, as well as the Hill-type SDSPs in Hill’s lunar problem. Double symmetries are exploited so that the SDSPs can be computed efficiently. The monodromy matrix can be calculated by the information of one fourth period. The periodicity conditions are solved by Broyden’s method with a line-search, and some numerical examples show that the scheme is very efficient. For a fixed period ratio and a given acute angle, there exist sixteen cases of initial values. For the restricted three-body problem, the cases of “Copenhagen problem” and the Sun–Jupiter–asteroid model are considered. New SDSPs are also numerically found in Hill’s lunar problem. Though the period ratio should be small theoretically, some new periodic orbits are found when the ratio is not too small, and the linear stability of the searched SDSPs is numerically determined.

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Section: Introductionmentioning

confidence: 99%

Determination of the doubly symmetric periodic orbits in the restricted three-body problem and Hill’s lunar problem

2023

Celest Mech Dyn Astron

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Dynamics in the Charged Restricted Circular Three-Body Problem

et al. 2017

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The existence and stability of periodic solutions for different types of perturbations associated to the Charged Restricted Circular Three Body Problem (shortly, CHRCTBP) is tackled using reduction and averaging theories as well as the technique of continuation of Poincaré for the study of symmetric periodic solutions. The determination of KAM 2-tori encasing some of the linearly stable periodic solutions is proved. Finally, we analyze the occurrence of Hamiltonian-Hopf bifurcations associated to some equilibrium points of the CHRCTBP. 2 and L coll 3 and the isosceles triangle equilibrium L iso 4 and L iso 5 were characterized

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Critical points of the integral map of the charged three-body problem

Hoveijn

Waalkens

Zaman

2019

Indagationes Mathematicae

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This is the first in a series of three papers where we study the integral manifolds of the charged three-body problem. The integral manifolds are the fibers of the map of integrals. Their topological type may change at critical values of the map of integrals. Due to the non-compactness of the integral manifolds one has to take into account besides 'ordinary' critical points also critical points at infinity. In the present paper we concentrate on 'ordinary' critical points and in particular elucidate their connection to central configurations. In a second paper we will study critical points at infinity. The implications for the Hill regions, i.e. the projections of the integral manifolds to configuration space, are the subject of a third paper.

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Schubart Solutions in the Charged Collinear Three-Body Problem

Cited by 5 publications

References 13 publications

Determination of the doubly symmetric periodic orbits in the restricted three-body problem and Hill’s lunar problem

Determination of the doubly symmetric periodic orbits in the restricted three-body problem and Hill’s lunar problem

Dynamics in the Charged Restricted Circular Three-Body Problem

Critical points of the integral map of the charged three-body problem

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