G. N. Yakovenko, “Orbits in the two-body problem in terms of symmetries”, Computer Research and Modeling, 2011, Volume 3, Issue 1,Pages <nobr>39

MATHEMATICAL MODELING AND NUMERICAL SIMULATION

Orbits in the two-body problem in terms of symmetries

G. N. Yakovenko

Moscow Institute of Physics and Technology (State University), 9 Institutsky street, Dolgoprudny, 141700, Russia

Abstract: For the two-body problem computed 12-parameter group symmetry transformations which translate the obvious solution — uniform motion of bodies in circular orbits with a common fixed center — a motion with arbitrary initial data.

Keywords: two-body problem, a symmetry transformation, elliptical orbit, the parabolic orbit, hyperbolic orbit.

UDC: 517.91.1

Received: 07.03.2011

DOI: 10.20537/2076-7633-2011-3-1-39-45