  The main objective for this research was the analytical exploration of the
dynamics of planar satellite rotation during the motion of an elliptical orbit
around a planet. First, we revisit the results of J. Wisdom et al. (1984), in
which, by the elegant change of variables (considering the true anomaly f as
the independent variable), the governing equation of satellite rotation takes
the form of an Abel ODE of the second kind, a sort of generalization of the
Riccati ODE. We note that due to the special character of solutions of a
Riccati-type ODE, there exists the possibility of sudden jumping in the
magnitude of the solution at some moment of time. In the physical sense, this
jumping of the Riccati-type solutions of the governing ODE could be associated
with the effect of sudden acceleration/deceleration in the satellite rotation
around the chosen principle axis at a definite moment of parametric time. This
means that there exists not only a chaotic satellite rotation regime (as per
the results of J. Wisdom et al. (1984)), but a kind of gradient catastrophe
(Arnold 1992) could occur during the satellite rotation process. We especially
note that if a gradient catastrophe could occur, this does not mean that it
must occur: such a possibility depends on the initial conditions. In addition,
we obtained asymptotical solutions that manifest a quasi-periodic character
even with the strong simplifying assumptions e ~ 0, p = 1, which reduce the
governing equation of J. Wisdom et al. (1984) to a kind of Beletskii equation.
