Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Has the Problem of the Motion of a Heavy Symmetric Top Been Solved in Quadratures?

Version 1 : Received: 8 June 2023 / Approved: 9 June 2023 / Online: 9 June 2023 (10:42:38 CEST)

How to cite: Deriglazov, A.A. Has the Problem of the Motion of a Heavy Symmetric Top Been Solved in Quadratures?. Preprints 2023, 2023060702. https://doi.org/10.20944/preprints202306.0702.v1 Deriglazov, A.A. Has the Problem of the Motion of a Heavy Symmetric Top Been Solved in Quadratures?. Preprints 2023, 2023060702. https://doi.org/10.20944/preprints202306.0702.v1

Abstract

We have revised the problem of the motion of a heavy symmetric top. When formulating equations of motion 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 rigid body. Using the Liouville's theorem, we solve the improved equations in quadratures and present the explicit expressions for the resulting elliptic integrals.

Keywords

Integrability; Lagrange top; Hamiltonian systems; Liouville's theorem

Subject

Physical Sciences, Mathematical Physics

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