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Hyperperiods, Orbital Stability, and Solution of the Problem of Kirkwood Gaps

Published online by Cambridge University Press:  14 August 2015

T. Kiang
T. Kiang*
Affiliation:
Dunsink Observatory, Castleknock, County Dublin, Ireland

Extract

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I believe I have solved, at least in principle, the long-standing problem of the Kirkwood gaps, and have incidentally initiated a new approach to questions of orbital stability. I shall begin with the concept I call hyperperiod. A given periodic dynamical system S with period P may or may not have a latent long period - the hyperperiod P∗. If P∗ exists, then any small displacement or variation, actual or virtual, once-for-all or recurrent, will induce a displacement y which will be periodic with period P∗ and will be of bounded amplitudes. We can then say that S is stable. If P∗ dose not exist, then y will eventually become indefinitely large - and we say that S is unstable.

Type
Part V: Minor Planets
Information
Symposium - International Astronomical Union , Volume 81: Dynamics of the Solar System , 1979 , pp. 227 - 230
Copyright
Copyright © Reidel 1979 

References

1. Kiang, T., Mon. Not. R. Astron. Soc. 162 (1973) 271–287.Google Scholar
2. Kiang, T., Nature, 273 (1978) 734–736.Google Scholar
3. Kiang, T., Paper VI. 8 of this Symposium.Google Scholar
4. Hill, G.W., Acta Math. 8 (1886) 1–36.CrossRefGoogle Scholar
5. Nacozy, P.E., Paper I.2 of this Symposium.Google Scholar