Va. Antonov et Ft. Shamshiev, CASES OF A STARS PLANAR MOTION INTEGRATED IN THE GRAVITATIONAL-FIELD OF A ROTATING SYSTEM, Celestial mechanics & dynamical astronomy, 59(3), 1994, pp. 209-219
The paper deals with some special cases of the existence of a local in
tegral of motion in a two-dimensional potential field rotating with co
nstant angular velocity. In this case the trajectories may be complete
ly determined, which is not always possible in other cases with a loca
l integral, in contrast to the cases with a true integral. Some cases
where the trajectories can be determined analytically are trivial but
there are also some new nontrivial cases.