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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Gauge Functions for Forces and Nonlinearities in Classical Oscillators

Journal of Applied Nonlinear Dynamics 13(4) (2024) 835--846 | DOI:10.5890/JAND.2024.12.015

L. C. Vestal, Z. E. Musielak

Department of Physics, University of Texas at Arlington, Arlington, TX 76019, USA

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Abstract

The abundance of gauge functions in dynamics is compelling because the total derivative of any scalar function can become a null Lagrangian, which makes the Euler-Lagrange equation identically zero. Thus, gauge functions have no direct effects on the resulting equations of motion. However, there is a special family of gauge functions that can be related directly to forces and nonlinearities in dynamical systems by using a method developed in this paper. To identify this special family, general gauge functions are constructed for second-order ordinary differential equations of motion describing one-dimensional dynamical systems. The gauge functions corresponding to forces and nonlinearities in a variety of known oscillators, including the Duffing oscillator, are presented, and the novel roles these functions play in classical dynamics are discussed.

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