Saturn's moon Hyperion is shaped like a battered potato and rides a stretched orbit, and as a result it has no fixed day. Its rotation is genuinely chaotic: gravity wrenches its long axis around unpredictably, tumbling end over end. Below, the moon orbits and spins on the left; on the right, a Poincaré section records its orientation once per orbit. Click the section to drop new trajectories and map the chaos.
Poincaré section orientation θ vs spin θ′, sampled at perihelion
Map the section and a structure appears: closed loops (locked rotations) marooned inside a grey fog of chaotic points where spin is unpredictable.
Order and chaos togetherDrag eccentricity toward 0 or asphericity down: the fog clears and the loops take over. A round moon on a circular orbit just spins steadily.
Why most moons don't tumbleThis isn't a toy result. Hyperion's chaotic rotation was predicted in 1984, and Cassini measured its real spin on close flybys in 2005.
The actual moon