Two-body problems with drag or thrust: Qualitative results (Q1568160)

The author considers two-body problems in with drag is proportional to the velocity divided by the square of distance, and whose radial and tangential components have distinct coefficients. A qualitative study of the equations of motion of two-body problems with a generalized drag is performed. The collision singularity in the equations of motions is removed by using suitable space- and time-rescaling transformations. The author studies an invariant set of rectilinear orbits and shows that only four cases are possible: attractive motion with radial drag, attractive motion with radial thrust, repelling motion with radial drag, and repelling motion with radial thrust. In each case the author examines in detail the properties of solutions: existence of collision-ejection, collision-escape, capture-collision, capture-escape, and oscillatory rectilinear orbits, and additionally the motion near collisions.