The (2,2,1) heavy top: a pure-precession regime
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911304212545536 |
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| author | Mityushov, E. |
| author_facet | Mityushov, E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05527 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The (2,2,1) heavy top: a pure-precession regime Mityushov, E. Exactly Solvable and Integrable Systems 2020 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. |
| title | The (2,2,1) heavy top: a pure-precession regime |
| topic | Exactly Solvable and Integrable Systems 2020 |
| url | https://arxiv.org/abs/2512.05527 |