nutation
/ noo-TAY-shun /
Nutation is the up-and-down nodding of a spinning axis, superimposed on its slower circular precession. Watch a heavy top that is leaning over and precessing: its tip does not sweep a perfectly smooth horizontal circle. Instead it bobs -- rising and dipping -- tracing a scalloped or looping path. That bobbing in the tilt angle is nutation, from the Latin for 'nodding'.
Precisely, nutation is the oscillation of the polar tilt angle theta (the second Euler angle) about its average value, while the precession is the steady drift of the azimuthal angle phi. For a heavy symmetric top the energy and the two conserved angular momenta constrain theta to oscillate between two turning angles theta_min and theta_max; the axis precesses forward while theta cycles between them, producing the familiar cusped or wavy trace. A top gently released from rest starts with a sharp cusp; one given a push can loop. In the idealized steady precession that most textbooks first present, the nutation amplitude is exactly zero and theta is held constant.
You see nutation in fast-spinning tops (small, quick wobbles that friction soon damps into smooth precession), in gyroscopes recovering from a disturbance, and in the Earth's axis: superimposed on the 26000-year precession of the equinoxes is an 18.6-year astronomical nutation of about 9 arcseconds, caused by the tilt and slow turning of the Moon's orbit. Nutation is the transient, oscillatory partner to the steady precession.
Release a gyroscope's axis from rest at a tilt and it does not glide smoothly into precession; it first dips, catching itself, then rises, in a rapid nod before friction smooths it out. That initial nod is nutation, the system's oscillation as it finds its steady precessing state.
Nutation is the oscillation of the tilt angle; precession is the steady drift of the azimuth.
Nutation and precession are two different Euler-angle motions, not two names for the same thing: nutation is theta oscillating, precession is phi advancing. A common wobble is really both happening at once.