1. The problem statement, all variables and given/known data Show that every trajectory, except r = 0, is asymptotically orbitally stable 2. Relevant equations I have a hint that: I should think of two initially close trajectories (say a(0) = |x(0) - y(0)| sufficiently small and see how the difference evolves over time (the rate a'(t).) I need to make |x(t)-y(t)| bounded. 3. The attempt at a solution I think I'm getting confused by the symbology and I'm not sure how to operate the equations. First I tried to calculate the fixed points. The only fixed point I get is the origin, r = 0. (If I tried r = 1, then I cant get theta ' = 0, so r = 0 must be the fixed point to look at, I'm guessing.) So, next, I can see that r' = r(1-r) will go to zero as r increases in value. I think that's something I'm looking for. Next, I think I need theta' to be bounded. Well, I know the first part, 1 + sin^2, will always be less than 2.....but there's nothing to bound (1-r)^2. As r increases, the term will just keep increasing without bound.... These are my thoughts on the problem so far and I don't know where to go with it from here...... Thanks for any help!