The finite dimension property of small oscillations of a top with a cavity filled with an ideal fluid (Q1392313)

The authors considers the title problem assuming that the cavity and the top are bodies of revolution with a common symmetry axis. The governing equations can be reduced to a linear differential equation in Hilbert space \(H\), where for the determination of the motion of the solid shell it is sufficient to restrict the above equation to a subspace \(L\subset H\). The main result of the paper can be formulated as follows: Let the cavity be a bounded connected domain that has a nonempty intersection with the symmetric axis. Then \(L\) is finite-dimensional if and only if the cavity is either the region enclosed between two concentric homothetic ellipsoids of revolution or an ellipsoid of revolution.