Astronomy and Astrophysics – Astronomy
Scientific paper
Sep 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986mnras.222..287g&link_type=abstract
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 222, Sept. 15, 1986, p. 287-297.
Astronomy and Astrophysics
Astronomy
5
Orbit Calculation, Orbit Perturbation, Phase-Space Integral, Stellar Orbits, Stochastic Processes, Hamiltonian Functions, Milky Way Galaxy
Scientific paper
Small perturbations of an integrable potential generally destroy the nonclassical integrals of motion and introduce layers of stochastic orbits in the phase-space of the perturbed Hamiltonian. This phenomenon may be shown to occur by Melnikov's (1963) method, and the Melnikov integrals may also be used to estimate the importance of the resulting stochastic layer, i.e., its width in phase-space. This depends strongly upon the type of perturbation. In this paper earlier work on two-dimensional galaxy potentials is generalized. In the general (n greater than or equal to 3) case, a vector of Melnikov integrals must be computed. A canonically invariant form is given here and shown to be equivalent to the standard formulation in reduced phase-space. This allows application of the method to three-dimensional Staeckel (1980) potentials.
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