Non-restricted double-averaged three body problem in Hill's case |
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| Authors: | M L Lidov S L Ziglin |
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| Institution: | (1) Institute of Applied Mathematics, Academy of Science of the USSR, Moscow, USSR;(2) Moscow State University, USSR |
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| Abstract: | A limiting case of the problem of three bodies (m
0,m
1,m
2) is considered. The distance between the bodiesm
0 andm
1 is assumed to be much less than that between their barycenter and the bodym
2 so that one may use Hill's approximation for the potential of interaction between the bodiesm
1 andm
2. In the absence of resonant relations the potential, double-averaged by the mean longitudes ofm
1 andm
2, describes the secular evolution of the orbits in the first approximation of the perturbation theory.As Harrington has shown, this problem is integrable. In the present paper a qualitative investigation of the evolution of the orbits and comparison with the analogous case in the restricted problem are carried out.The set of initial data is found, for which a collision between the bodiesm
0 andm
1 takes place.The region of the parameters of the problem is determined, for which plane retrograde motion is unstable.In a special example the results of approximate analysis are compared with those of numerical integration of the exact equations of the three body problem.
                          m
0,m
1,m
2.  ,  m
0 m
1.   m
2,   m
1 m
2  m
1 m
2   .  , .   .   , m
0 m
1. , .  .
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| Keywords: | |
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