Three Families Of Integrals Which Arise In Some Three Body Problems
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Author | : John R. Jasperse |
Publisher | : |
Total Pages | : 40 |
Release | : 1967 |
Genre | : Coulomb functions |
ISBN | : |
Three families of integrals that arise in the three-body problem with Coulomb pair potentials are examined. Two of the families are definite integrals on a single variable where the integrands are products of two Coulomb Sturmian functions. The third family is a triple integral where the integrands are products of four Coulomb Sturmian functions and two Legendre polynomials. Closed-form expressions are derived for all the integrals, except for one subset of the most general triple integral. An outline of the procedure necessary to obtain a closed expression for this subset is given. (Author).
Author | : John R. Jasperse |
Publisher | : |
Total Pages | : 32 |
Release | : 1967 |
Genre | : Coulomb functions |
ISBN | : |
Three families of integrals that arise in the three-body problem with Coulomb pair potentials are examined. Two of the families are definite integrals on a single variable where the integrands are products of two Coulomb Sturmian functions. The third family is a triple integral where the integrands are products of four Coulomb Sturmian functions and two Legendre polynomials. Closed-form expressions are derived for all the integrals, except for one subset of the most general triple integral. An outline of the procedure necessary to obtain a closed expression for this subset is given. (Author).
Author | : C. Marchal |
Publisher | : Elsevier |
Total Pages | : 593 |
Release | : 2012-12-02 |
Genre | : Science |
ISBN | : 0444600744 |
Recent 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.
Author | : |
Publisher | : |
Total Pages | : 1264 |
Release | : 1967 |
Genre | : Aeronautics |
ISBN | : |
Author | : |
Publisher | : |
Total Pages | : 956 |
Release | : 1988 |
Genre | : Aeronautics |
ISBN | : |
Author | : |
Publisher | : |
Total Pages | : 1352 |
Release | : 1967 |
Genre | : Government publications |
ISBN | : |
Author | : Defense Documentation Center (U.S.) |
Publisher | : |
Total Pages | : 784 |
Release | : 1967 |
Genre | : Science |
ISBN | : |
Author | : |
Publisher | : |
Total Pages | : 224 |
Release | : 1967 |
Genre | : Science |
ISBN | : |
Author | : |
Publisher | : |
Total Pages | : 896 |
Release | : 1970-11 |
Genre | : Science |
ISBN | : |
Author | : Eunice C. Cronin |
Publisher | : |
Total Pages | : 644 |
Release | : 1972 |
Genre | : Military research |
ISBN | : |
A systems analysis technique is applied to the scientific problem solving requirements of a major Air Force research organization to establish: The functional organization of a research support group; A valuable data base for a Customer User Library (CUL); and A Management Information System for scheduling, reporting and control. The report summarizes the functional organization of the Analysis and Simulation Branch of the Computation Center at AFCRL as derived from an analysis of the spectrum of analytical and computational problems originating in the Laboratories. A detailed description the structure and mode of operation of the Customer User Library is provided, together with a discussion of the associated Management Information System. An extensive listing of scientific problem abstracts is provided in the Appendices.