Dynamics of a particle moving along an orbital tower

A simple analysis of the dynamics of a particle moving along an orbital tower was discussed. It was observed that at synchronous radius, there existed a hyperbolic fixed point which resulted in an unstable equilibrium and a potential barrier that a particle must cross. It was shown that the addition of friction did not remove the hyperbolic fixed point, but modified its instability timescale. It was also shown that the friction lead to phase paths converging asymptotically to a single manifold in the phase space of the problem.