## Explanation: parameters of the Earth rotation

Orientation of the Earth in the inertial space is defined by a 3-dimenensional function of time. There is more than one way to parameterize that function. The Network Earth Rotation Service provides the following parameters on the specified moment of time at scale TAI:
 UTC minus TAI The differences between UTC function and TAI. NB: UTC is NOT time, but a non-differentiable function of time. Units: secobds UT1 minus TAI Parameter UT1 describes orientation of the Earth with respect to the axis of its rotation. It is defined as a prturbational ngle with respect to a uniform rotation with nominal angular velocity 7.292115146706979 · 10-5 rad/sec. Units: seconds. X pole coordinate Parameter X pole coordinate describes the offset of the Earth's pole in the crust-fixed coordinate system along the Greenwich meridian towards axis X. Units: arcseconds. Y pole coordinate Parameter Y pole coordinate describes the offset of the Earth's pole in the crust-fixed coordinate system along the meridian 90° west, opposite to axis Y. Units: arcseconds. Nutation offset Δψ Nutation offset Δε Euler angle 1 Euler angle with respect to axis 1. Does not take into account harmonic terms. Units: rad. Euler angle 2 Euler angle with respect to axis 2. Does not take into account harmonic terms. Units: rad. Euler angle 3 Perturbation of the Euler angle with respect to axis 3 after subtraction a linear trend with angular velocity 7.292115146706979 · 10-5 rad/sec. Does not take into account harmonic terms with periods less than 4 days. Units: rad. Length of day UT1 rate X pole rate Rate of change of X pole coordinate. Units: arcsec/day. Y pole rate Rate of change of Y pole coordinate. Units: arcsec/day. Rotation matrix 3 × 3 rotation matrix that tranforms a vector in the crust-rfixed coordinate system in to the inertial coordinate system for accounting the Earth rotation. The order of nine terms: (1,1), (2,1), (3,1), (1,2), (2,2), (3,2), (1,3), (2,3), (3,3) Units: dimensionless. Rotation matrix rate Time derivative of the 3 × 3 rotation matrix that transforms a vector in the crust-rfixed coordinate system in to the inertial coordinate system for accounting the Earth rotation. The order of nine terms: (1,1), (2,1), (3,1), (1,2), (2,2), (3,2), (1,3), (2,3), (3,3) Units: 1/s. Rotation matrix acceleration Second time derivative of the 3 × 3 rotation matrix that transforms a vector in the crust-rfixed coordinate system in to the inertial coordinate system for accounting the Earth rotation. The order of nine terms: (1,1), (2,1), (3,1), (1,2), (2,2), (3,2), (1,3), (2,3), (3,3) Units: 1/s2.

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