Motion in a Central Force Field with Drag or Tangential Propulsion

Motion of a particle in a central attractive force field is considered in the presence of a tangential force depending on the position and velocity of the particle. It is found that a certain critical speed characterizes orbits which are logarithmic spirals. Orbits are qualitatively different depending on whether the speed is everywhere greater or everywhere less than the critical speed. A condition on the tangential force implies that the motion can have two apses at most.