Publication Abstracts
Contopoulos and Moutsoulas 1966
Contopoulos, G., and M. Moutsoulas, 1966: Resonance cases and small divisors in a third integral of motion. III. Astron. J., 71, 687-698, doi:10.1086/110173.
This paper discusses two cases where small divisors play an important role in the third integral. The Hamiltonian used is H = (1/2)(X2+Y2+Ax2+By2)-εxy2 = h h. In the first case the two unperturbed frequencies are nearly equal. If ε is very small and we set B = A+Kε2 we find resonance phenomena when K is in the range ( -5h/3A2, 10h/3A2). For larger or smaller values of K all the orbits are boxes. This range is divided into four parts by the values K = -2h/3A2, K = 5h/6A2, and K = 7h/3A2. The forms of the invariant curves are different in the four intervals. The corresponding orbits are either box type, or similar to the orbits of the resonance case A =B, except for the D-type orbits, which appear only in the third and fourth intervals.
In the second case one unperturbed frequency is almost the double of the other. If we set 4B = A+ek we find resonance phenomena when -4(2h/A)1/2 < k < 4(2h/A)1/2. The boundaries of the orbits are approximately arcs of three parabolas, as in the resonance case.
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BibTeX Citation
@article{co07200r, author={Contopoulos, G. and Moutsoulas, M.}, title={Resonance cases and small divisors in a third integral of motion. III}, year={1966}, journal={Astronomical Journal}, volume={71}, pages={687--698}, doi={10.1086/110173}, }
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RIS Citation
TY - JOUR ID - co07200r AU - Contopoulos, G. AU - Moutsoulas, M. PY - 1966 TI - Resonance cases and small divisors in a third integral of motion. III JA - Astron. J. JO - Astronomical Journal VL - 71 SP - 687 EP - 698 DO - 10.1086/110173 ER -
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