On the motion of the principal axes of inertia within an elastic tri-axial earth

Astronomy and Astrophysics – Astronomy

Scientific paper

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Earth Axis, Earth Rotation, Earth Tides, Elastic Deformation, Inertia, Triaxial Stresses, Elastic Bodies, Linear Equations, Liouville Equations, Love Waves, Magnetic Equator, Magnetic Poles, Terradynamics

Scientific paper

The behavior of the principal axes of inertia under the influence of both rotational and tidal deformations of an elastic triaxial earth is studied in detail. The development of directional cosines for all three axes with respect to the mean Tisserand axes are derived for the earth model with Love number 0.29. It is shown that the amplitude of the equatorial component of teh motion of both equatorial axes is about two orders of magnitude greater than the amplitude of the motion of the polar axis, and that it can reach almost 12 km at the surface of the earth. The polar axis describes a spiral whose amplitude varies with an approximately 14-day period, executing roughly one revolution per day. Over a one-day period, both equatorial axes describe an open figure eight whose equatorial amplitude also varies with a 14-day period.

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