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arXiv · 1305.0016

Retrograde resonance in the planar three-body problem

M. H. M. Morais·F. Namouni
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Abstract

We continue the investigation of the dynamics of retrograde resonances initiated in Morais & Giuppone (2012). After deriving a procedure to deduce the retrograde resonance terms from the standard expansion of the three-dimensional disturbing function, we concentrate on the planar problem and construct surfaces of section that explore phase-space in the vicinity of the main retrograde resonances (2/-1, 1/-1 and 1/-2). In the case of the 1/-1 resonance for which the standard expansion is not adequate to describe the dynamics, we develop a semi-analytic model based on numerical averaging of the unexpanded disturbing function, and show that the predicted libration modes are in agreement with the behavior seen in the surfaces of section.

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M. H. M. Morais, F. Namouni. 2013-09-24. Retrograde resonance in the planar three-body problem. https://doi.org/10.1007/s10569-013-9519-2

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