(Wisdom, Pearle, and Mignard ,1983)

"Most Hamiltonian systems display both regular and irregular trajectories. The phase space is divided; there are regions in which trajectories behave chaotically and regions where trajectories are quasiperiodic (Hénon and Heiles, 1964). The simplest and most intuitive method of determining whether a trajectory is chaotic or quasiperiodic is the surface of section method. The spin-orbit problem, as defined in the last section, is 2[;\pi;] periodic in the dimensionless time. A surface of section is obtained by looking at the system stroboscopically with period 2[;\pi;]. A natural choice for the section is to plot d[;\vartheta;]/dt versus [;\vartheta;] at every periapse passage. The successive points define smooth curves for quasiperiodic trajectories; for chaotic trajectories the points appear to fill an area on the section in an apparently random manner. It is a remarkable property of Hamiltonian systems that these two types of behavior are usually readily distinguishable and that they are generally both present on any surface of section."

Taken from here.

The surface of section method, is also called a Poincaré map in phase space. For symbolic exact solutions in dynamical systems, even with erroneous ideas one gets the right answer. On the other hand, chaotic motion requires more care, than most students exercise. In this case the use of an algebraic program translation step is important.

Write what you mean, otherwise the computer will go in undesired trajectories.

Coming back to Wisdom et al..:

"If this chaotic tumbling is confirmed, Hyperion will be the first example of chaotic behavior among the permanent members of the solar system."

What a way to finish a paper!