Variations in Earth rotation: Solution of the EULER-LIOUVILLE equation as a boundary value problem

Abstract

The earth does not rotate uniformly: the deviation of its angular velocity vector ω(t) from a constant one ω in an earth-fixed reference system B is described by three time-dependent earth rotation parameters (see [2]):

• The deviation of the direction of ω(t) expressed by two coordinates m₁(t) and m₂(t), is called called polar motion. On the other hand, the deviation of the length of ω(t) can be expressed by the variation of the length of day, denoted by m₃(t). It is decoupled from polar motion and will not be considered here.

• Polar motion describes the position of the “true” rotation pole compared to a conventional terrestrial pole (CTP) “fixed” to the earth and strictly related to B. However, the CTP (and B) is defined somewhat arbitrarily by convention, usually indirectly by coordinates of a set of observation stations. In Fig. 1.1, the CTP is the origin of the coordinate system in the (m_1,m₂)- plane, and the rotation pole describes a spiraling curve in this plane.

• Today, earth rotation parameters can be observed at high precision. They are needed for transforming coordinates from earth-fixed to space-fixed reference systems, a task frequently performed for evaluation of space geodesy observations. Moreover, as all mass movements related to geodynamic, meteorologic or oceanographic processes enter the angular momentum budget, earth rotation parameters can be an indicator for these processes, the time series are suitable to test geophysical models and estimate parameters.