On rotation invariant integrable systems

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Abstract

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.

About the authors

Andrey Vladimirovich Tsiganov

Steklov Mathematical Institute of Russian Academy of Sciences

Email: a.tsyganov@spbu.ru
ORCID iD: 0000-0001-7228-9593
SPIN-code: 3084-6239
Scopus Author ID: 7003435326
ResearcherId: B-4674-2011
Doctor of physico-mathematical sciences, Associate professor

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