Periodic orbits in the general three-body problem and the relationship between them

Орлов, В. В.; Петрова, А. В.; Rubinov, A.; Martynova, A. I.

doi:10.1134/1.1738158

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…The structures found correspond qualitatively to zones of departure after the first, second, and third triple encounter found by Tanikawa and Umehara [17]. Similar structures in the domain D also arose in other studies of the free-fall three-body problem [18,19]. Analysis of the trajectories of bodies in individual zones of rapid departures show the complex structures of these zones.…”

Section: Resultsmentioning

confidence: 50%

The decay of triple systems

Martynova

Орлов

2014

Astron. Rep.

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Numerical simulations have been carried out in the general three-body problem with equal masses with zero initial velocities, to investigate the distribution of the decay times T based on a representative sample of initial conditions. The distribution has a power-law character on long time scales, f (T ) ∝ T −α , with α = 1.74. Over small times T < 30T cr (T cr is the mean crossing time for a component of the triple system), a series of local maxima separated by about 1.0T cr is observed in the decay-time distribution. These local peaks correspond to zones of decay after one or a few triple encounters. Figures showing the arrangement of these zones in the domain of the initial conditions are presented.

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Section: Resultsmentioning

confidence: 50%

The decay of triple systems

Martynova

Орлов

2014

Astron. Rep.

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“…These regions are concentrated in the zones of regular motions in the vicinities of stable periodic orbits. (iii) The dynamic evolution of plane non-rotating triple systems for which the initial conditions were specified in such a way that one of the bodies is located at the centre of mass of the triple system has also been investigated [55]. (iv) The dynamic evolution of 120 000 equal-mass rotating triple systems has been examined, too.…”

Section: Dynamic Evolutionmentioning

confidence: 99%

A tertiary component in close binary systems

Rovithis‐Livaniou

2007

Astronomical & Astrophysical Transactions

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In this short review, the existence of third bodies in close binary systems is presented. Starting with the observational methods used to detect the tertiary component, we continue with the theoretical studies concerning the stability and evolution of triple systems and also of multiple systems in general. We next consider the type of tertiary component and give a list of catalogues for these systems; we end with a general discussion.

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On “generalized Kepler’s third law” and mass dependence of periods of three-body orbits

Raonić

Dmitrašinović

2021

Meccanica

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Periodic orbits in the general three-body problem and the relationship between them

Cited by 3 publications

References 8 publications

The decay of triple systems

The decay of triple systems

A tertiary component in close binary systems

On “generalized Kepler’s third law” and mass dependence of periods of three-body orbits

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