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arXiv · 2512.05527

The (2,2,1) heavy top: a pure-precession regime

E. Mityushov
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Abstract

This work develops a curvature-based geometric formulation of the Euler-Poisson equations by lifting the dynamics to the 3-sphere S^3 equipped with the left-invariant metric induced by the inertia tensor. For the inertia ratio I = (2,2,1) and r = (0,0,1), the curvature balance reveals a distinguished pure-precession regime: a nontrivial family of motions in which the tilt angle gamma_3 remains constant and the dynamics reduce to uniform precession with explicit trigonometric solutions. The family is characterized and derived explicitly, and a Lax representation is obtained. This regime illustrates how geometric lifting and curvature balance can isolate simplified dynamical structures even inside non-integrable systems. In addition, we briefly discuss the role of a numerical symmetry detection procedure based on curvature forcing, which guided the identification of the (2,2,1) parameters as geometrically distinguished.

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E. Mityushov. 2025-12-05. The (2,2,1) heavy top: a pure-precession regime. https://arxiv.org/abs/2512.05527

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