Periodic orbits in the general three-body problem and the relationship between them |
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| Authors: | V V Orlov A V Petrova A V Rubinov A I Martynova |
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| Institution: | (1) Astronomical Institute, St. Petersburg State University, Universitetskii pr. 28, St. Petersburg, Peterhof, 198504, Russia;(2) St. Petersburg Academy of Forestry Engineering, Institutskii per. 5, St. Petersburg, 194021, Russia |
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| Abstract: | We study the regions of finite motions in the vicinity of three simple stable periodic orbits in the general problem of three equal-mass bodies with a zero angular momentum. Their distinctive feature is that one of the moving bodies periodically passes through the center of mass of the triple system. We consider the dynamical evolution of plane nonrotating triple systems for which the initial conditions are specified in such a way that one of the bodies is located at the center of mass of the triple system. The initial conditions can then be specified by three parameters: the virial coefficient k and the two angles, φ1 and φ2, that characterize the orientation of the velocity vectors for the bodies. We scanned the region of variation in these parameters k∈(0, 1); φ1, φ2∈(0, π) at steps of δk=0.01; δφ1=δφ2=1° and identified the regions of finite motions surrounding the periodic orbits. These regions are isolated from one another in the space of parameters (k, φ1, φ2). There are bridges that correspond to unstable orbits with long lifetimes between the regions. During the evolution of these metastable systems, the phase trajectory can “stick” to the vicinity of one of the periodic orbits or move from one vicinity to another. The evolution of metastable systems ends with their breakup. |
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| Keywords: | celestial mechanics three-body problem periodic orbits |
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