# On “pathological oscillations” of rotating fluids in the theory of nutation

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## Summary

"Pathological oscillations" of rotating fluids occur when the period of oscillations with respect to a mobile reference frame exceeds half of a rotational period. The oscillations of such kind play an important role in the theory of nutation of a real Earth model with compressible, heterogeneous outer liquid core and solid inner core. In this paper we try to present a sufficiently rigorous description of such oscillations.

The full system of two-dimensional solutions is found numerically. Results are presented in form of infinite matrices which connect the coefficients of spherical harmonic expansions of the boundary conditions, pressure, and horizontal components of tidal velocities. The substitution of these known solutions in the three-dimensional equations of motion results in an infinite set of ordinary differential equations which describe the conditions of equilibrium in the radial direction. Below we analize"pathological" oscillations of different kind which are described by this set of equations.

## Keywords

Reference Frame Radial Direction Horizontal Component Earth Model Inner Core## Preview

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