The Chandler wobble is an example of the kind of motion that can occur for a freely rotating object that is not a sphere; this is called a free nutation.
Somewhat confusingly, the direction of the Earth's rotation axis relative to the stars also varies with different periods, and these motions—caused by the tidal forces of the Moon and Sun—are also called nutations, except for the slowest, which are precessions of the equinoxes.
The existence of Earth's free nutation was predicted by Isaac Newton in Corollaries 20 to 22 of Proposition 66, Book 1 of the Philosophiæ Naturalis Principia Mathematica, and by Leonhard Euler in 1765 as part of his studies of the dynamics of rotating bodies.
[2] Since the Earth is not a rigid body, the Chandler wobble should die down with a time constant of about 68 years,[6] a very short period compared to geological timescales.
While it must be due to changes in the mass distribution or angular momentum of the Earth's outer core, atmosphere, oceans, or crust (from earthquakes), for a long time the actual source was unclear, since no available motions seemed to be coherent with what was driving the wobble.