Geodesic
Geometry of invariant manifolds of a gyroscope in the field of a quadratic potential
Izvestiya. Mathematics , Tome 37 (1991) no. 1, pp. 227-242

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Real formulas are found (in terms of Prym $\theta$-functions) for the equation of rotation of a gyroscope in a field with an arbitrary quadratic potential. The number of components of the solutions are computed, depending on the “spectral data” of the problem. 
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     title = {Geometry of invariant manifolds of a gyroscope in the field of a quadratic potential},
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A. I. Zhivkov. Geometry of invariant manifolds of a gyroscope in the field of a quadratic potential. Izvestiya. Mathematics , Tome 37 (1991) no. 1, pp. 227-242. http://geodesic.mathdoc.fr/item/IM2_1991_37_1_a9/