One Integrable Case of the Perturbed Two-Body Problem

The motion of a particle in a perturbed gravitational field of a point mass is considered. A constant force is taken as a perturbation. The L-matrix is selected in such a manner that in regular coordinates the separation of variables takes place. Integration of the equations of motion of the problem under consideration is carried out. The solutions are expressed in terms of elliptic functions. A qualitative investigation of the integrals of motion is made, and numerical examples are presented.     

The motion of a particle in perturbed field of an attracting center

The integrable case of the perturbed two-body problem is considered. The perturbation is determined by the potential of a special form. The L-matrix is chosen in such a way that partial separation of variables should take place in regular coordinates. Integration of the equations of motion of the problem under consideration is made. The solutions are expressed through elliptic functions. The orbits for various cases are constructed. The results of numerical calculations are given.     

The family of potentials admitting integration of the perturbed two-body problem in regular coordinates

An infinite system of potentials is presented that admits separation of regular variables in the perturbed two-body problem. The regular coordinates are constructed using a specially selected L-matrix. An explicit solution to the problem in the elliptical case is constructed. In the general case the solution is reduced to inversion of hyper-elliptic integrals. The cases of motion with and without constraints are considered. The results of numerical experiments are presented.