Geodesic
The action variable and frequency of a relativistic harmonic oscillator
Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 3, pp. 408-415 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present three series representations of the frequency of a relativistic harmonic oscillator. The first two representations use two equivalent forms of the action variable. The third representation involves determining its period by direct integration. The energy dependance of the oscillator frequency is manifestly seen in all three representations. We demonstrate that all three forms yield the same expression for the frequency in the case of the weakly relativistic oscillator and have an identical nonrelativistic limit.
Keywords: Hamilton–Jacobi theory, relativity, simple harmonic oscillator.
Mots-clés : action variable 
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M. K. Balasubramanya. The action variable and frequency of a relativistic harmonic oscillator. Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 3, pp. 408-415. http://geodesic.mathdoc.fr/item/TMF_2010_162_3_a5/

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