caa a22 4500 445863471 CHVBK 20180317145450.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10569-011-9358-y doi (NATIONALLICENCE)springer-10.1007/s10569-011-9358-y Existence and stability of symmetric periodic simultaneous binary collision orbits in the planar pairwise symmetric four-body problem [Elektronische Daten] [Lennard Bakker, Tiancheng Ouyang, Duokui Yan, Skyler Simmons] We analytically prove the existence of a symmetric periodic simultaneous binary collision orbit in a regularized planar pairwise symmetric equal mass four-body problem. This is an extension of our previous proof of the analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized planar fully symmetric equal mass four-body problem. We then use a continuation method to numerically find symmetric periodic simultaneous binary collision orbits in a regularized planar pairwise symmetric 1, m, 1, m four-body problem for m between 0 and 1. Numerical estimates of the the characteristic multipliers show that these periodic orbits are linearly stability when 0.54≤ m≤ 1, and are linearly unstable when 0<m≤0.53. Springer Science+Business Media B.V., 2011 N-body problem nationallicence Regularization nationallicence Periodic orbits nationallicence Stability nationallicence Simultaneous binary collision nationallicence Bakker Lennard Department of Mathematics, Brigham Young University, 84602, Provo, UT, USA aut Ouyang Tiancheng Department of Mathematics, Brigham Young University, 84602, Provo, UT, USA aut Yan Duokui Chern Institute of Mathematics, Nankai University, 300071, Tianjin, People's Republic of China aut Simmons Skyler Department of Mathematics, Brigham Young University, 84602, Provo, UT, USA aut Celestial Mechanics and Dynamical Astronomy Springer Netherlands 110/3(2011-07-01), 271-290 0923-2958 110:3<271 2011 110 10569 https://doi.org/10.1007/s10569-011-9358-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10569-011-9358-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bakker Lennard Department of Mathematics, Brigham Young University, 84602, Provo, UT, USA aut NATIONALLICENCE 700 1- Ouyang Tiancheng Department of Mathematics, Brigham Young University, 84602, Provo, UT, USA aut NATIONALLICENCE 700 1- Yan Duokui Chern Institute of Mathematics, Nankai University, 300071, Tianjin, People's Republic of China aut NATIONALLICENCE 700 1- Simmons Skyler Department of Mathematics, Brigham Young University, 84602, Provo, UT, USA aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Springer Netherlands 110/3(2011-07-01), 271-290 0923-2958 110:3<271 2011 110 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer