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Integrable Systems in Celestial Mechanics

2008-12-15 Science
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Release : 2008-12-15
Genre : Science
Kind : eBook
Book Rating : 950/5 ( reviews)

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Book Synopsis Integrable Systems in Celestial Mechanics by : Diarmuid Ó'Mathúna

Download or read book Integrable Systems in Celestial Mechanics written by Diarmuid Ó'Mathúna. This book was released on 2008-12-15. Available in PDF, EPUB and Kindle. Book excerpt: Shows that exact solutions to the Kepler (two-body), the Euler (two-fixed center), and the Vinti (earth-satellite) problems can all be put in a form that admits the general representation of the orbits and follows a definite shared pattern Includes a full analysis of the planar Euler problem via a clear generalization of the form of the solution in the Kepler case Original insights that have hithertofore not appeared in book form

Theory of Orbits

2003-10-08 Science
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Release : 2003-10-08
Genre : Science
Kind : eBook
Book Rating : 631/5 ( reviews)

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Book Synopsis Theory of Orbits by : Dino Boccaletti

Download or read book Theory of Orbits written by Dino Boccaletti. This book was released on 2003-10-08. Available in PDF, EPUB and Kindle. Book excerpt: Half a century ago, S. Chandrasekhar wrote these words in the preface to his l celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ ... J Indeed, several of the problems of modern stellar dy namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con sidered from the point of view of celestial mechanics (the N-body problem with N » 1), fluid mechanics (the system is represented by a material con tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).

Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature

2013-04-17 Science
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Release : 2013-04-17
Genre : Science
Kind : eBook
Book Rating : 035/5 ( reviews)

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Book Synopsis Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature by : T.G. Vozmischeva

Download or read book Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature written by T.G. Vozmischeva. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: Introd uction The problem of integrability or nonintegrability of dynamical systems is one of the central problems of mathematics and mechanics. Integrable cases are of considerable interest, since, by examining them, one can study general laws of behavior for the solutions of these systems. The classical approach to studying dynamical systems assumes a search for explicit formulas for the solutions of motion equations and then their analysis. This approach stimulated the development of new areas in mathematics, such as the al gebraic integration and the theory of elliptic and theta functions. In spite of this, the qualitative methods of studying dynamical systems are much actual. It was Poincare who founded the qualitative theory of differential equa tions. Poincare, working out qualitative methods, studied the problems of celestial mechanics and cosmology in which it is especially important to understand the behavior of trajectories of motion, i.e., the solutions of differential equations at infinite time. Namely, beginning from Poincare systems of equations (in connection with the study of the problems of ce lestial mechanics), the right-hand parts of which don't depend explicitly on the independent variable of time, i.e., dynamical systems, are studied.

Mathematical Aspects of Classical and Celestial Mechanics

2007-07-05 Mathematics
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Release : 2007-07-05
Genre : Mathematics
Kind : eBook
Book Rating : 266/5 ( reviews)

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Book Synopsis Mathematical Aspects of Classical and Celestial Mechanics by : Vladimir I. Arnold

Download or read book Mathematical Aspects of Classical and Celestial Mechanics written by Vladimir I. Arnold. This book was released on 2007-07-05. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.

Dynamical Systems VII

2013-12-14 Mathematics
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Release : 2013-12-14
Genre : Mathematics
Kind : eBook
Book Rating : 96X/5 ( reviews)

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Book Synopsis Dynamical Systems VII by : V.I. Arnol'd

Download or read book Dynamical Systems VII written by V.I. Arnol'd. This book was released on 2013-12-14. Available in PDF, EPUB and Kindle. Book excerpt: A collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.

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