For orbit calculation, see Earth Orientation Parameters (EOP).
Polar motion is the movement of the rotation axis with respect to the crust of the Earth [1].
Components
Polar motion consits of two major motions: Chandler wobble and annual wobble. Chandler wobble is the free motion with the period of about 435 days. Annual wobble is the forced motion excited predominantly by atmospheric dynamics. These two motions beat each other and results in the secular variation in the direction of 80th meridian east [2].
Observations
Polar motion is observed by International Earth Rotation and Reference System Service (IERS). IERS defines polar motion as the motion of Celestial Intermediate Pole (CIP) with respect to the International Terrestrial Reference System (ITRS) [3].

References
[1] Seidelmann, P. K. (1982). 1980 IAU theory of nutation: The final report of the IAU working group on nutation. Celestial Mechanics, 27, 79-106. https://doi.org/10.1007/BF01228952
[2] Polar Motion. International Earth Rotation and Reference System Service. https://www.iers.org/IERS/EN/Science/EarthRotation/PolarMotion.html
[3] Petit, G., Luzum, B. IERS Conventions (2010). https://www.iers.org/IERS/EN/Publications/TechnicalNotes/tn36.html
Related Souces
Chandler, S. C., On the variation of the latitude, I, Astron. J., 11, 59–61,
1891a.
Chandler, S. C., On the variation of the latitude, II, Astron. J., 11, 65–70,
1891b.
Earth Orientation Center. Observatorie de Paris. https://hpiers.obspm.fr/eop-pc/index.php