An asymmetric heavy gyroscope can regularly precess only when its suspension point lies on one of two lines marking where the intermediate and largest moments of inertia exchange order, with exactly two motions.
Has the problem of the motion of a heavy symmetric top been solved in quadratures?
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We have revised the problem of the motion of a heavy symmetric top. When formulating equations of the Lagrange top with the diagonal inertia tensor, the potential energy has more complicated form as compared with that assumed in the literature on dynamics of a rotating body. This implies the corresponding improvements in equations of motion. Using the Liouville's theorem, we solve the improved equations in quadratures and present the explicit expressions for the resulting elliptic integrals.
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An alternative interpretation of the Grioli gyroscope suspension points
An asymmetric heavy gyroscope can regularly precess only when its suspension point lies on one of two lines marking where the intermediate and largest moments of inertia exchange order, with exactly two motions.