Equivalence theorem between position-dependent mass dynamics and classically conservative dynamics

Variable-mass problems do not as a rule fit into the cardinal formulation of mechanics; therefore, new formalism has been constructed to treat variable-mass dynamics. We aim to situate a class of position-dependent mass problems in the level of classically conservative dynamics. The issue is that, by nature, the sum of kinetic and potential energies of a position-dependent mass point is not preserved. Given that, we demonstrate a theorem which establishes the mathematical equivalence between position-dependent mass dynamics and classically conservative dynamics. Meshchersky's equation is herein assumed to be in scalar form. In applying the theorem, a counterintuitive situation arises. To our very best knowledge, our contribution is novel in the field of variable-mass dynamics.