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Bertrand’s theorem and virial theorem in fractional classical mechanics

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Abstract.

Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.

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Correspondence to Rui-Yan Yu.

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Yu, RY., Wang, T. Bertrand’s theorem and virial theorem in fractional classical mechanics. Eur. Phys. J. Plus 132, 386 (2017). https://doi.org/10.1140/epjp/i2017-11639-9

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  • DOI: https://doi.org/10.1140/epjp/i2017-11639-9

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