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Found all equivalence classes for electromagnetic potentials and space-timemetrics of Stackel spaces, provided that the equations of motion of theclassical charged test particles are integrated by the method of completeseparation of variables in the Hamilton-Jacobi equation. Separation is carriedout using the complete sets of mutually-commuting integrals of motion of type(2.1), whereby in a privileged coordinate system the Hamilton-Jacobi equationturns into a parabolic type equation.

Separation of variables in Hamilton-Jacobi equation for a charged test particle in the Stackel spaces of type (2.1)