Systems of Kowalevski type and discriminantly separable polynomials. (English) Zbl 1357.37081

A famous integrable case of the rigid body motion around a fixed point is the Kowalevski top. There is a large literature dedicated to understanding Kowalevski’s original integration procedure. In a recent paper by one of the authors, a new approach to the Kowalevski integration procedure has been suggested. Its novelty lies in the introduction of the new notion of discriminantly separable polynomials. Here, it is shown that by using discriminantly separable polynomials of degree two in each of three base variables of the problem, it is possible to construct a class of integrable dynamical systems so that all main steps of the Kowalevski’s integration procedure follow as easy and transparent logical consequences. Some new examples are discussed.


37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
70E17 Motion of a rigid body with a fixed point
70E40 Integrable cases of motion in rigid body dynamics
14H70 Relationships between algebraic curves and integrable systems
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