  Starting from the notion of discriminantly separable polynomials of degree
two in each of three variables, we construct a class of integrable dynamical
systems. These systems can be integrated explicitly in genus two
theta-functions in a procedure which is similar to the classical one for the
Kowalevski top. The discriminnatly separable polynomials play the role of the
Kowalevski fundamental equation. The natural examples include the Sokolov
systems and the Jurdjevic elasticae.
