Physics
Scientific paper
Jul 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978cemec..18...51b&link_type=abstract
Celestial Mechanics, Volume 18, Issue 1, pp.51-101
Physics
3
Scientific paper
We consider the plane circular restricted problem for μ=0. We continue here the study begun in Brjuno (1972b) of the characteristics of families of solutions with consecutive collisions (familiesS andT N ). The equation of the characteristics (2.13), connecting the variablesa, e, θ only, is obtained in Section 2A. In Section 2B, we introduce instead oftilde e a new variablee * such that the equation of the characteristics takes the form (2.19), detailed in Theorem 2.2. This allows a full explanation of the structure of the set of characteristics fora>1. An additional analysis is given fora<1 (Section 2E). In Section 3 we consider the values of the Jacobi constant along the characteristics of familiesS. The extremal points are found (Section 3C) and, the arithmetic properties of the extremal points and of the points of intersection are discussed. Some unsolved problems are mentioned.
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