Comment on 'Nonlinear dynamics of a position-dependent mass-driven Duffing-type oscillator' - Mustafa, Omar (IOP Publishing, 2013)
Using a generalized coordinate along with a proper invertible coordinate transformation, we show that the Euler–Lagrange equation used by Bagchi et al (2013 J. Phys. A: Math. Theor. 46 032001) is in clear violation of Hamilton's principle. We also show that the Newton equation of motion they have used is not in a form that satisfies the dynamics of position-dependent mass (PDM) settings. The equivalence between the Euler–Lagrange equation and Newton's equation is now proved and documented through the proper invertible coordinate transformation and the introduction of a new PDM byproducted reaction-type force. The total mechanical energy for the PDM is shown to be conservative (i.e., dE/dt = 0, unlike Bagchi et al's (2013) observation).
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Keywords: PHYSICS; MULTIDISCIPLINARY; MATHEMATICAL; POTENTIALS