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Using a generalized coordinate along with a proper invertible coordinatetransformation, we show that the Euler-Lagrange equation used by Bagchi et al.16 is in clear violation of the Hamilton's principle. We also show thatNewton's equation of motion they have used is not in a form that satisfies thedynamics of position-dependent mass (PDM) settings.. The equivalence betweenEuler-Lagrange's and Newton's equations is now proved and documented throughthe proper invertible coordinate transformation and the introduction of a newPDM byproducted reaction-type force. The total mechanical energy for the PDM isshown to be conservative (i.e., dE/dt=0, unlike Bagchi et al.'s 16observation).

On the nonlinear dynamics of a position-dependent mass-driven Duffing-type oscillator: Lagrange and Newton equations' equivalence