The "Nutation Rosette":

When a spacecraft nutates (oscillates), the spin axis tip moves creating a rosette pattern. This animation shows the Ulysses nutation at one second intervals.

The "Nutation Spin Axis":

This animation represents the spin axis by an imaginary laser beam, and shows the nutation rosette as it would appear projected on an imaginary screen.

The spin axis goes around one full rosette in about 48 seconds. Meanwhile the spacecraft continues to rotate around the spin axis at a rate approximately 4 times faster (once every 12 seconds).