On rotation invariant integrable systems
- Autores: Tsiganov A.V.1
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Afiliações:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Edição: Volume 88, Nº 2 (2024)
- Páginas: 206-226
- Seção: Articles
- URL: https://bakhtiniada.ru/1607-0046/article/view/254269
- DOI: https://doi.org/10.4213/im9506
- ID: 254269
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Resumo
The problem of finding the first integrals of the Newton equations inthe $n$-dimensional Euclidean space is reduced to that of findingtwo integrals of motion on the Lie algebra $\mathrm{so}(4)$which are invariant under $m\geqslant n-2$ rotation symmetry fields.As an example, we obtainseveral families of integrable and superintegrable systems with first,second, and fourth-degree integrals of motion in the momenta.The corresponding Hamilton–Jacobi equationdoes not admit separation variables in any of the known curvilinear orthogonal coordinate systemsin the Euclidean space.
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Sobre autores
Andrey Tsiganov
Steklov Mathematical Institute of Russian Academy of Sciences
Email: a.tsyganov@spbu.ru
ORCID ID: 0000-0001-7228-9593
Código SPIN: 3084-6239
Scopus Author ID: 7003435326
Researcher ID: B-4674-2011
Doctor of physico-mathematical sciences, Associate professor
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