We present a class of “ellipsoidal rotation matrices” which can be used to characterise tectonic plate motion; where geocentric Cartesian coordinates travel along paths tangential to the ellipsoid. We contrast them with conventional Euler pole plate motion models which are more closely aligned with spherical coordinate systems and inherently induce a change in geodetic ellipsoidal height. We demonstrate the use of each in the Indo-Australian tectonic plate setting, which is known to move approximately 7 cm/yr in a north-northeast direction. Geocentric Datum of Australia 2020 (GDA2020) coordinates are “plate-fixed” static coordinates obtained using a conventional Euler pole plate motion model to align time dependent coordinates with the 2014 realisation of the International Terrestrial Reference Frame (ITRF) at the epoch 2020.0. We show that this Euler pole plate motion model can introduce ellipsoidal height velocities of up to -0.2 mm/yr. This is small but systematic, so pertinent for consideration with high accuracy vertical land motion studies using GDA2020 coordinates. We further investigate the comparative statistical accuracy of conventional Euler pole and the ellipsoidal models with respect to characterising plate motion captured in high quality GNSS data.