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arXiv · 2305.12370

Rotations and integrability

A. V. Tsiganov
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Abstract

We discuss some families of integrable and superintegrable systems in $n$-dimensional Euclidean space which are invariant to $m\geq n-2$ rotations. The integrable invariant Hamiltonian $H=\sum p_i^2+V(q)$ commutes with $n-2$ integrals of motion $M_α$ and an additional integral of motion $G$, which are polynomials of first and fourth-order in momenta, respectively.

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A. V. Tsiganov. 2024-11-06. Rotations and integrability. https://arxiv.org/abs/2305.12370

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