Inna Basak
Barcelona, E08028 Spain
Department de Matematica Aplicada I,
Universitat Politecnica de Catalunya
Publications:
Fedorov Y. N., Basak I.
Separation of Variables and Explicit Thetafunction Solution of the Classical Steklov–Lyapunov Systems: A Geometric and Algebraic Geometric Background
2011, vol. 16, nos. 34, pp. 374395
Abstract
The paper revises the explicit integration of the classical Steklov–Lyapunov systems via separation of variables, which had been first made by F. Kötter in 1900, but was not well understood until recently. We give a geometric interpretation of the separating variables and then, applying the Weierstrass hyperelliptic root functions, obtain explicit thetafunction solution to the problem. We also analyze the structure of poles of the solution on the Jacobian on the corresponding hyperelliptic curve. This enables us to obtain a solution for an alternative set of phase variables of the systems that has a specific compact form.
In conclusion we discuss the problem of integration of the Rubanovsky gyroscopic generalizations of the above systems. 
Basak I.
Bifurcation analysis of the Zhukovskii–Volterra system via biHamiltonian approach
2010, vol. 15, no. 6, pp. 677684
Abstract
The main goal of this paper consists of bifurcation analysis of classical integrable Zhukovskii–Volterra system. We use the fact that the ZV system is biHamiltonian and apply new techniques [1] for analysis of singularities of biHamiltonian systems, which can be formulated as follows: the structure of singularities of a biHamiltonian system is determined by that of the corresponding compatible Poisson brackets.

Basak I.
Explicit Solution of the Zhukovski–Volterra Gyrostat
2009, vol. 14, no. 2, pp. 223236
Abstract
The paper is devoted to explicit integration of the classical generalization of the Euler top: the Zhukovski–Volterra system describing the free motion of a gyrostat. We revise the solution for the components of the angular momentum first obtained by Volterra in [1] and present an alternative solution based on an algebraic parametrization of the invariant curves. This also enables us to derive an effective description of the motion of the body in space.
