In mechanics of the mass point passage from one frame of reference to another moving with velocity $\vec{u}$ consists in subtracting this vector from the velocity of the particle. In general case the vector $\vec{u}$ is not constant, as, for example, when passing through a rotating frame, this operation creates inertial forces. Analysis of this phenomenon from the point of view of Lagrangian and Hamiltonian mechanics is interesting from the general relativistic point of view due to Einstein's principle of equivalence. We show that the vector $\vec{u}$ plays the role of vector potential which, however, essentially differs from vector potential known in classical electrodynamics. Comparative analysis of the two kinds of vector potentials is completed.