5 papers
Classical R-matrices for generalized so(p,q) tops
Andrey Tsiganov
An integrable deformation of the known integrable model of two interacting p-dimensional and q-dimensional spherical tops is considered. After reduction this system gives rise to t…
Commutative Poisson subalgebras for the Sklyanin bracket and deformations of known integrable models
V. V. Sokolov, A. V. Tsiganov
A hierarchy of commutative Poisson subalgebras for the Sklyanin bracket is proposed. Each of the subalgebras provides a complete set of integrals in involution with respect to the…
On the Lax pairs for the generalized Kowalewski and Goryachev-Chaplygin tops
Vladimir V. Sokolov, Andrey V. Tsiganov
A polynomial deformation of the Kowalewski top is considered. This deformation includes as a degeneration a new integrable case for the Kirchhoff equations found recently by one of…
The Maupertuis principle and integrable systems
Andrey Tsiganov
We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric f…
The Stackel systems and algebraic curves
A. V. Tsiganov
We show how the Abel-Jacobi map provides all the principal properties of an ample family of integrable mechanical systems associated to hyperelliptic curves. We prove that derivati…