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Central forces depending on the distance only. Case where all the bounded orbits are periodic

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Abstract

It is shown in this paper that the only potentials corresponding to central force for which all the bounded orbits are periodic are the potential of the harmonic oscillator and of the two body problem. A discussion is given in the case where a circular orbit exists and when the orbits near the circular orbit are periodic.

We calculate in these cases the angle between pericentre and apocentre.Celestial Mechanics

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References

  • Arnold, V. I.: (1978),Mathematical Methods of Classical Mechanics, Springer Verlag, pp. 37–38.

  • Bertrand, J.: ‘Théorème relatif au mouvement d'un point attiré vers un centre fixe’,Comptes rendus de l'Académie des Sciences, t. LXXVII.

  • Tisserand, F.: (1889),Traité de Mécanique Céleste, Gauthier-Villars, t. I, p. 43.

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  1. Catholic University of Louvain, Belgium

    Jacques Roels & Christine Aerts

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  1. Jacques Roels
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  2. Christine Aerts
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Roels, J., Aerts, C. Central forces depending on the distance only. Case where all the bounded orbits are periodic. Celestial Mechanics 44, 77–85 (1988). https://doi.org/10.1007/BF01230708

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  • DOI: https://doi.org/10.1007/BF01230708

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