Product Description: Thework described in this has somewhat erratically,over monograph grown, of than a more interest inthe was firstaroused period thirty My subject years. thebeautiful and inBroucke.'sthesis also by see computations drawings (1963; Broucke where familiesof orbits in the restricted three 1968), periodic body for the Earth Moon ratio = were mass problem investigated (/...read more

Product Description: hereafter calledvolume the of In a volume study previous (H6non 1997, I), the restricted initiated. families in problem (We generating three body was recallthat families defined asthe limits offamilies of are periodic generating determinationof orbitsfor Themain wasfoundto lieinthe 4 problem p 0...read more

Product Description: Henri Poincare (1854-1912) was one of the greatest scientists of his time, perhaps the last one to have mastered and expanded almost all areas in mathematics and theoretical physics. He created new mathematical branches, such as algebraic topology, dynamical systems, and automorphic functions, and he opened the way to complex analysis with several variables and to the modern approach to asymptotic expansions...read more

Product Description: KAM theory is a powerful tool apt to prove perpetual stability in Hamiltonian systems, which are a perturbation of integrable ones. The smallness requirements for its applicability are well known to be extremely stringent. A long standing problem, in this context, is the application of KAM theory to ""physical systems"" for ""observable"" values of the perturbation parameters...read more

Product Description: How do three celestial bodies move under their mutual gravitational attraction? This problem has been studied by Isaac Newton and leading mathematicians over the last two centuries. Poincaré's conclusion, that the problem represents an example of chaos in nature, opens the new possibility of using a statistical approach...read more

It is well known that the restricted three-body problem has triangular equilibrium points. These points are linearly stable for values of the mass parameter,, below Routh's critical value, 1. It is also known that in the spatial case they are nonlinearly stable, not for all the initial conditions in a neighborhood of the equilibrium points L4, L5 but for a set of relatively large measures. This follows from the celebrated Kolmogorov-;Arnold-;Moser theorem. In fact there are neighborhoods of computable size for which one obtains practical stability in the sense that the massless particle remains close to the equilibrium point for a big time interval (some millions of years, for example).According to the literature, what has been done in the problem follows two approaches: (a) numerical simulations of more or less accurate models of the real solar system; (b) study of periodic or quasi-periodic orbits of some much simpler problem.The concrete questions that are studied in this volume are: (a) Is there some orbit of the real solar system which looks like the periodic orbits of the second approach? (That is, are there orbits performing revolutions around L4 covering eventually a thick strip? Furthermore, it would be good if those orbits turn out to be quasi-periodic. However, there is no guarantee that such orbits exist or will be quasi-periodic). (b) If the orbit of (a) exists and two particles (spacecraft) are put close to it, how do the mutual distance and orientation change with time?As a final conclusion of the work, there is evidence that orbits moving in a somewhat big annulus around L4 and L5 exist, that these orbits have small components out of the plane of the Earth-;Moon system, and that they are at most mildly unstable." (view table of contents)

Product Description: Cost estimating is a powerful tool in industry and business. Anyone involved in cost estimating will find this book extremely useful because of the real life examples, which mean they can use the information in real situations immediately. (view table of contents, read Amazon.com's description)

Product Description: The aim of this book is to explain, analyze and compute the kinds of motions that appear in an extended vicinity of the geometrically defined equilateral points of the Earth-;Moon system, as a source of possible nominal orbits for future space missions...read more (view table of contents, read Amazon.com's description)

Product Description: The phase space of the spatial three-body problem is an open subset in ${\mathbb R}^{18}$. Holding the ten classical integrals of energy, center of mass, linear and angular momentum fixed defines an eight dimensional submanifold. For fixed nonzero angular momentum, the topology of this manifold depends only on the energy...read more

Product Description: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics...read more

Product Description: Nuclear physics is undoubtedly a many-body problem. A nice introduction into the present status of this subject may be found in the comprehensive mono­ graph by P. Ring and P. Schuck "The Nuclear Many-Body Problem" (Springer, Berlin, Heidelberg, New York 1980)...read more

Product Description: 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...read more