TY - JOUR

T1 - On rotation invariant integrable systems

AU - Tsiganov, A.V.

PY - 2024

Y1 - 2024

N2 - The problem of finding the first integrals of the Newton equations in the $n$-dimensional Euclidean space is reduced to that of finding two integrals of motion on the Lie algebra $\mathrm{so}(4)$ which are invariant under $m\geq n-2$ rotation symmetry fields. As an example, we obtain several families of integrable and superintegrable systems with first, second, and fourth-degree integrals of motion in the momenta. The corresponding Hamilton-Jacobi equation does not admit separation variables in any of the known curvilinear orthogonal coordinate systems in the Euclidean space.

AB - The problem of finding the first integrals of the Newton equations in the $n$-dimensional Euclidean space is reduced to that of finding two integrals of motion on the Lie algebra $\mathrm{so}(4)$ which are invariant under $m\geq n-2$ rotation symmetry fields. As an example, we obtain several families of integrable and superintegrable systems with first, second, and fourth-degree integrals of motion in the momenta. The corresponding Hamilton-Jacobi equation does not admit separation variables in any of the known curvilinear orthogonal coordinate systems in the Euclidean space.

UR - https://www.mendeley.com/catalogue/3a00dce5-7e1d-30cc-ac1c-ab45b50faabb/

U2 - 10.4213/im9506e

DO - 10.4213/im9506e

M3 - Article

VL - 88

SP - 389

EP - 409

JO - Izvestiya Mathematics

JF - Izvestiya Mathematics

SN - 1064-5632

IS - 2

ER -