The theory of tensor invariants of ordinary differential equations and Cartan's classification of simple Lie algebras are used to establish the isomorphism of the Kozlov problem on the motion of a ferromagnetic in a magnetic field and the Shottky problem on the motion of a four-dimensional solid. Also new polynomial and rational Poisson bivectors invariant either with respect to a pair of commuting phase flows or invariant with respect to one of a pair of flows are found.