Application of the theory of Hill's equation to the study of the stability of periodic classical orbits
- 21 July 1989
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 22 (14) , L673-L676
- https://doi.org/10.1088/0305-4470/22/14/004
Abstract
The theory of Hill's equation is applied to periodic orbits in a classical model of the magnetic hydrogen atom. It is shown how an infinite Hill determinant may be approximated and computed, thus giving the discriminant of the relevant Whittaker-Hill equation. This discriminant supplies information on the stability of the above periodic orbits which is much more easily obtained than by the numerical integrations of the orbits appearing in previous publications. The method is also applicable to other classical systems of current interest.Keywords
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