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

Daniel de la Fuente ^[1] ; Pedro J. Torres ^[1]
1. [1] Universidad de Granada
  
  Universidad de Granada
  
  Granada, España
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 3, 2017, págs. 579-589
Idioma: inglés
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Resumen
- 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.