A New Relativistic Extension of the Harmonic Oscillator Satisfying an Isochronicity Principle

  1. Daniel de la Fuente 1
  2. Pedro J. Torres 1
  1. 1 Universidad de Granada
    info

    Universidad de Granada

    Granada, España

    ROR https://ror.org/04njjy449

Journal:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Year of publication: 2017

Volume: 16

Issue: 3

Pages: 579-589

Type: Article

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Abstract

A new relativistic extension of the one-dimensional simple harmonic oscillator is presented. The equations of motion express the proportionality between the relativistic force acting on a particle and the distance to the oscillation center measured by a comoving observer with the particle, instead of the distance measured by a certain inertial observer. The resulting trajectory is really harmonic, i.e., the ‘proper period’ of the oscillations does not depend on the amplitude, against the anharmonicity of the standard relativistic harmonic oscillator.

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