Physics
Scientific paper
Jul 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974cemec...9..471k&link_type=abstract
Celestial Mechanics, Volume 9, Issue 4, pp.471-481
Physics
1
Scientific paper
The instability criterion of a nonlinear mechanical system neutral to the first approximation is formulated for the internal resonance case which is characterized by the existence of commensurabilities between the frequencies of the system. The criterion derived is used for determining the regions of instability of Laplace's constant triangular solutions of the unrestricted three-body problem. It is shown that in the region where necessary Routh-Joukovsky's stability conditions are satisfied there may exist eight resonanceunstable sets of the masses of the three bodies. These sets may be mechanically interpreted as follows: in the case of resonance instability the barycentre of the equilateral triangle formed by the three bodies is located on one of the eight circles constructed in the geometrical centre of this triangle.
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