Transformation of amplitudes and frequencies of precession and nutation of the earth’s rotation vector to amplitudes and frequencies of diurnal polar motion |
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| Authors: | Burghard Richter Johannes Engels Erik Grafarend |
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| Institution: | 1. Deutsches Geod?tisches Forschungsinstitut, Alfons-Goppel-Strasse 11, 80539, Munich, Germany
2. Geod?tisches Institut, Universit?t Stuttgart, Geschwister-Scholl-Strasse 24D, 70174, Stuttgart, Germany
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| Abstract: | The temporal change of the rotation vector of a rotating body is, in the first order, identical in a space-fixed system and
in a body-fixed system. Therefore, if the motion of the rotation axis of the earth relative to a space-fixed system is given
as a function of time, it should be possible to compute its motion relative to an earth-fixed system, and vice versa. This
paper presents such a transformation. Two models of motion of the rotation axis in the space-fixed system are considered:
one consisting only of a regular (i.e., strictly conical) precession and one extended by circular nutation components, which
are superimposed upon the regular precession. The Euler angles describing the orientation of the earth-fixed system with respect
to the space-fixed system are derived by an analytical solution of the kinematical Eulerian differential equations. In the
first case (precession only), this is directly possible, and in the second case (precession and nutation), a solution is achieved
by a perturbation approach, where the result of the first case serves as an approximation and nutation is regarded as a small
perturbation, which is treated in a linearized form. The transformation by means of these Euler angles shows that the rotation
axis performs in the earth-fixed system retrograde conical revolutions with small amplitudes, namely one revolution with a
period of one sidereal day corresponding to precession and one revolution with a period which is slightly smaller or larger
than one sidereal day corresponding to each (prograde or retrograde) circular nutation component. The peculiar feature of
the derivation presented here is the analytical solution of the Eulerian differential equations. |
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