caa a22 4500 445863390 CHVBK 20180317145450.0 cr unu---uuuuu 170323e20110501xx s 000 0 eng 10.1007/s10569-011-9338-2 doi (NATIONALLICENCE)springer-10.1007/s10569-011-9338-2 Families of symmetric relative periodic orbits originating from the circular Euler solution in the isosceles three-body problem [Elektronische Daten] [Mitsuru Shibayama, Kazuyuki Yagasaki] We study symmetric relative periodic orbits in the isosceles three-body problem using theoretical and numerical approaches. We first prove that another family of symmetric relative periodic orbits is born from the circular Euler solution besides the elliptic Euler solutions. Previous studies also showed that there exist infinitely many families of symmetric relative periodic orbits which are born from heteroclinic connections between triple collisions as well as planar periodic orbits with binary collisions. We carry out numerical continuation analyses of symmetric relative periodic orbits, and observe abundant families of symmetric relative periodic orbits bifurcating from the two families born from the circular Euler solution. As the angular momentum tends to zero, many of the numerically observed families converge to heteroclinic connections between triple collisions or planar periodic orbits with binary collisions described in the previous results, while some of them converge to "previously unknown” periodic orbits in the planar problem. Springer Science+Business Media B.V., 2011 Three-body problem nationallicence Relative periodic orbit nationallicence Symmetric periodic orbit nationallicence Bifurcation nationallicence Euler solution nationallicence Shibayama Mitsuru Research Institute for Mathematical Sciences, Kyoto University, 606-8502, Kyoto, Japan aut Yagasaki Kazuyuki Mathematics Division, Department of Information Engineering, Niigata University, 950-2181, Niigata, Japan aut Celestial Mechanics and Dynamical Astronomy Springer Netherlands 110/1(2011-05-01), 53-70 0923-2958 110:1<53 2011 110 10569 https://doi.org/10.1007/s10569-011-9338-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10569-011-9338-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shibayama Mitsuru Research Institute for Mathematical Sciences, Kyoto University, 606-8502, Kyoto, Japan aut NATIONALLICENCE 700 1- Yagasaki Kazuyuki Mathematics Division, Department of Information Engineering, Niigata University, 950-2181, Niigata, Japan aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Springer Netherlands 110/1(2011-05-01), 53-70 0923-2958 110:1<53 2011 110 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer