The Three-Body ProblemRecent research on the theory of perturbations, the analytical approach and the quantitative analysis of the three-body problem have reached a high degree of perfection. The use of electronics has aided developments in quantitative analysis and has helped to disclose the extreme complexity of the set of solutions. This accelerated progress has given new orientation and impetus to the qualitative analysis that is so complementary to the quantitative analysis. The book begins with the various formulations of the three-body problem, the main classical results and the important questions and conjectures involved in this subject. The main part of the book describes the remarkable progress achieved in qualitative analysis which has shed new light on the three-body problem. It deals with questions such as escapes, captures, periodic orbits, stability, chaotic motions, Arnold diffusion, etc. The most recent tests of escape have yielded very impressive results and border very close on the true limits of escape, showing the domain of bounded motions to be much smaller than was expected. An entirely new picture of the three-body problem is emerging, and the book reports on this recent progress. The structure of the solutions for the three-body problem lead to a general conjecture governing the picture of solutions for all Hamiltonian problems. The periodic, quasi-periodic and almost-periodic solutions form the basis for the set of solutions and separate the chaotic solutions from the open solutions. |
From inside the book
Results 1-3 of 45
... eccentricity e and the ratio of the two major masses . This conclusion can be extended to all Eulerian motions since the three masses only appear through the above constant whose range of variation , from 0 to 7 , is the same for the ...
... eccentricities and inclinations that imply large perturbations ... the eccentricity of Nereid is 0.75 ! 6 ) Finally , if the mutual inclination j is very large , in the vicinity of 90 ° , the perturbations of j and especially e es ...
... eccentricities and zero inclination ( second species ) and the orbits with small eccentricities and large mutual inclination ( third species ) . These three species are presented in the Fig . 52 , their construction will be discussed in ...
Contents
Summaries in eight languages | 1 |
History | 2 |
The law of universal attraction | 3 |
Copyright | |
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