Geodesic
Discriminantly separable polynomials and the generalized Kowalevski top
Theoretical and applied mechanics, Tome 44 (2017) no. 2.

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The notion of discriminantly separable polynomials of degree two in each of three variables has been recently introduced and related to a class of integrable dynamical systems. Explicit integration of such systems can be performed in a way similar to Kowalevski's original integration of the Kowalevski top. Here we present the role of discriminantly separable polynomials in integration of yet another well known integrable system, the so-called generalized Kowalevski top - the motion of a heavy rigid body about a fixed point in a double constant field. We present a novel way to obtain the separation variables for this system, based on the discriminantly separable polynomials.
Keywords: the generalized Kowalevski top, discriminantly separable polynomials, separation variables 
@article{TAM_2017_44_2_a8,
     author = {Vladimir Dragovi\'c and Katarina Kuki\'c},
     title = {Discriminantly separable polynomials and the generalized {Kowalevski} top},
     journal = {Theoretical and applied mechanics},
     pages = {229 - 236},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/TAM_2017_44_2_a8/}
}
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Vladimir Dragović; Katarina Kukić. Discriminantly separable polynomials and the generalized Kowalevski top. Theoretical and applied mechanics, Tome 44 (2017) no. 2. http://geodesic.mathdoc.fr/item/TAM_2017_44_2_a8/