2019/06/30 by Omar Mustafa
Engineering · Mathematics · Physics and Astronomy · #Algorithm #Classical mechanics #Equations of motion #Euler's formula #Geophysics and Sensor Technology #Linearizability #Mathematical analysis #Mathematics #Mechanical and Optical Resonators #Newtonian fluid #Nonlinear system #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Type (biology) #math-ph #math.MP
paper · pdf · doi:10.1088/1402-4896/ab825b
published as Phys. Scr. 95 (2020) 065214 (9p) · 11 pages, to appear in Physica Scripta
openalex publication_date 2020/03/23 · arxiv created 2020/03/24 · openalex created_date 2020/04/03 · arxiv updated 2020/07/02 · openalex updated_date 2026/08/05
Abstract We argue that, under multidimensional position-dependent mass (PDM) settings, the Euler–Lagrange textbook invariance falls short and turned out to be vividly incomplete and/or insecure for a set of PDM-Lagrangians. We show that the transition from Euler–Lagrange component presentation to Newtonian vector presentation is necessary and vital to guarantee invariance. The totality of the Newtonian vector equations of motion is shown to be more comprehensive and instructive than the Euler–Lagrange component equations of motion (they do not run into conflict with each other though). We have successfully used the Newtonian invariance amendment , along with some nonlocal space-time point transformation recipe, to linearize Euler–Lagrange equations and extract exact solutions for a set of n -dimensional nonlinear PDM-oscillators. They are, Mathews-Lakshmanan type-I PDM-oscillators, power-law type-I PDM-oscillators, the Mathews-Lakshmanan type-II PDM-oscillators, the power-law type-II PDM-oscillators, and some nonlinear shifted Mathews-Lakshmanan type-I PDM-oscillators.