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

Abstract

Using a generalized coordinate along with a proper invertible coordinate transformation, 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 that Newton's equation of motion they have used is not in a form that satisfies the dynamics of position-dependent mass (PDM) settings.. The equivalence between Euler-Lagrange's and Newton's equations 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 16 observation).

4 pages

References in corpus (7)

• Ordering ambiguity revisited via position dependent mass pseudo-momentum operators
• Quantum particles trapped in a position-dependent mass barrier; a d-dimensional recipe
• Position Dependent Mass Oscillators and Coherent States
• $\eta$-weak-Pseudo-Hermiticity generators and exact solvability
• Non-Hermitian von Roos Hamiltonian's $\eta$-weak-pseudo-Hermiticity, isospectrality and exact solvability
• Classical oscillator with position-dependent mass in a complex domain
• Non-Hermitian Hamiltonian versus E=0 localized states

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• n-dimensional PDM non-linear oscillators: Linearizability and Euler-Lagrange or Newtonian invariance
• Position-dependent mass charged particles in magnetic and Aharonov-Bohm flux fields: separability, exact and conditionally exact solvability
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• $n$-dimensional PDM-damped harmonic oscillators: Linearizability, and exact solvability
• Qualitative analysis of certain generalized classes of quadratic oscillator systems
• Dynamics of the Modified Emden and pseudo-Modified Emden Equations: position-dependent mass, invariance and exact solvability