TY - JOUR
T1 - From Brake to Syzygy
AU - Moeckel, Richard
AU - Montgomery, Richard
AU - Venturelli, Andrea
PY - 2012/6
Y1 - 2012/6
N2 - In the planar three-body problem, we study solutions with zero initial velocity (brake orbits). Following such a solution until the three masses become collinear (syzygy), we obtain a continuous, flow-induced Poincaré map. We study the image of the map in the set of collinear configurations and define a continuous extension to the Lagrange triple collision orbit. In addition, we provide a variational characterization of some of the resulting brake-to-syzygy orbits and find simple examples of periodic brake orbits.
AB - In the planar three-body problem, we study solutions with zero initial velocity (brake orbits). Following such a solution until the three masses become collinear (syzygy), we obtain a continuous, flow-induced Poincaré map. We study the image of the map in the set of collinear configurations and define a continuous extension to the Lagrange triple collision orbit. In addition, we provide a variational characterization of some of the resulting brake-to-syzygy orbits and find simple examples of periodic brake orbits.
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U2 - 10.1007/s00205-012-0502-y
DO - 10.1007/s00205-012-0502-y
M3 - Article
AN - SCOPUS:84861006874
SN - 0003-9527
VL - 204
SP - 1009
EP - 1060
JO - Archive For Rational Mechanics And Analysis
JF - Archive For Rational Mechanics And Analysis
IS - 3
ER -