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Isotropic three-dimensional oscillator in relativistic classical mechanics

The trajectory of the isotropic three-dimensional oscillator in relativistic classical mechanics is derived. Its form depends on the values of the angular momentum l. It is a rosette for 0 < l < l0 and a circle for l = l0, where l0 is the maximum value of the angular momentum for a given energy. According to expectation, in the non-relativistic limit, the rosette reduces to an ellipse.