Has the problem of the motion of a heavy symmetric top been solved in quadratures?

Abstract

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.

6 pages, typos fixed once again, notation improved, discussion extended

References in corpus (4)

• Lagrangian and Hamiltonian formulations of asymmetric rigid body, considered as a constrained system
• Geodesic motion on the symplectic leaf of $SO(3)$ with distorted $e(3)$ algebra and Liouville integrability of a free rigid body
• Poincaré-Chetaev equations in the Dirac's formalism of constrained systems
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Cited by in corpus (3)

• General solution to Euler-Poisson equations of a free symmetric body by direct summation of power series
• Lagrange top: integrability according to Liouville and examples of analytic solutions
• An alternative interpretation of the Grioli gyroscope suspension points