Astronomy and Astrophysics – Astrophysics
Scientific paper
Sep 1979
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979a%26a....78..195a&link_type=abstract
Astronomy and Astrophysics, vol. 78, no. 2, Sept. 1979, p. 195-199.
Astronomy and Astrophysics
Astrophysics
1
Celestial Mechanics, Gravitational Fields, Harmonic Oscillators, Orbital Mechanics, Time Dependence, Coupling, Equations Of Motion, Hamiltonian Functions, Numerical Integration
Scientific paper
Changes in the patterns of the trapping regions on the surface of section (x, derivative of x) in the case of two coupled harmonic oscillators with frequencies equal to the square roots of A and B are investigated for the case where the potential is time dependent. Special attention is given to the resonance cases where B tends exponentially or linearly in time to A or 1/4A. Numerical integration of the equations of motion indicates that in both resonance cases rotation of the pattern of the trapping regions for fast approach to resonance is a common phenomenon. It is found that: (1) in general, there are no qualitative changes in the corresponding patterns that depend on the manner in which the system tends to each resonance; (2) the pattern of the trapping regions for a fast approach to each resonance rotates about the origin by an angle given by a simple empirical formula; and (3) the initial pattern changes significantly when the system tends to each resonance very slowly.
Antonopoulos P.
Barbanis Basil
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