Generating Families In The Restricted Three Body Problem

Author : Michel Henon
Publisher : Springer Science & Business Media
ISBN 13 : 3540417338
Total Pages : 308 pages
Book Rating : 4.30/5 ( download)

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Download or read book Generating Families in the Restricted Three-Body Problem written by Michel Henon and published by Springer Science & Business Media. This book was released on 2001-04-24 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical restricted three-body problem is of fundamental importance because of its applications in astronomy and space navigation, and also as a simple model of a non-integrable Hamiltonian dynamical system. A central role is played by periodic orbits, of which many have been computed numerically. This is the second volume of an attempt to explain and organize the material through a systematic study of generating families, the limits of families of periodic orbits when the mass ratio of the two main bodies becomes vanishingly small. We use quantitative analysis in the vicinity of bifurcations of types 1 and 2. In most cases the junctions between branches can now be determined. A first-order approximation of families of periodic orbits in the vicinity of a bifurcation is also obtained. This book is intended for scientists and students interested in the restricted problem, in its applications to astronomy and space research, and in the theory of dynamical systems.

Author : Michel Henon
Publisher : Springer Science & Business Media
ISBN 13 : 3540696504
Total Pages : 282 pages
Book Rating : 4.06/5 ( download)

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Download or read book Generating Families in the Restricted Three-Body Problem written by Michel Henon and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical restricted problem of three bodies is of fundamental importance for its applications to astronomy and space navigation, and also as a simple model of a non-integrable Hamiltonian dynamical system. A central role is played by periodic orbits, of which a large number have been computed numerically. In this book an attempt is made to explain and organize this material through a systematic study of generating families, which are the limits of families of periodic orbits when the mass ratio of the two main bodies becomes vanishingly small. The most critical part is the study of bifurcations, where several families come together and it is necessary to determine how individual branches are joined. Many different cases must be distinguished and studied separately. Detailed recipes are given. Their use is illustrated by determining a number of generating families, associated with natural families of the restricted problem, and comparing them with numerical computations in the Earth-Moon and Sun-Jupiter case.

Author : Michel Henon
Publisher : Springer Science & Business Media
ISBN 13 : 3540447121
Total Pages : 308 pages
Book Rating : 4.22/5 ( download)

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Download or read book Generating Families in the Restricted Three-Body Problem written by Michel Henon and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical restricted three-body problem is of fundamental importance because of its applications in astronomy and space navigation, and also as a simple model of a non-integrable Hamiltonian dynamical system. A central role is played by periodic orbits, of which many have been computed numerically. This is the second volume of an attempt to explain and organize the material through a systematic study of generating families, the limits of families of periodic orbits when the mass ratio of the two main bodies becomes vanishingly small. We use quantitative analysis in the vicinity of bifurcations of types 1 and 2. In most cases the junctions between branches can now be determined. A first-order approximation of families of periodic orbits in the vicinity of a bifurcation is also obtained. This book is intended for scientists and students interested in the restricted problem, in its applications to astronomy and space research, and in the theory of dynamical systems.

Author : Michel Henon
Publisher : Springer
ISBN 13 : 9783540417330
Total Pages : 304 pages
Book Rating : 4.38/5 ( download)

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Download or read book Generating Families in the Restricted Three-Body Problem written by Michel Henon and published by Springer. This book was released on 2001-04-24 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Alexander D. Bruno
Publisher : Walter de Gruyter
ISBN 13 : 3110901730
Total Pages : 377 pages
Book Rating : 4.33/5 ( download)

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Download or read book The Restricted 3-Body Problem: Plane Periodic Orbits written by Alexander D. Bruno and published by Walter de Gruyter. This book was released on 2011-05-03 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Author : R. A. Broucke
Publisher :
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.35/5 ( download)

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Download or read book Periodic Orbits in the Elliptic Restricted Three-body Problem written by R. A. Broucke and published by . This book was released on 1969 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Urs Frauenfelder
Publisher : Springer
ISBN 13 : 3319722786
Total Pages : 374 pages
Book Rating : 4.88/5 ( download)

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Download or read book The Restricted Three-Body Problem and Holomorphic Curves written by Urs Frauenfelder and published by Springer. This book was released on 2018-08-29 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019

Author : Alessandra Celletti
Publisher : Springer Science & Business Media
ISBN 13 : 1402053258
Total Pages : 434 pages
Book Rating : 4.52/5 ( download)

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Download or read book Periodic, Quasi-Periodic and Chaotic Motions in Celestial Mechanics: Theory and Applications written by Alessandra Celletti and published by Springer Science & Business Media. This book was released on 2007-02-02 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides the most recent advances of Celestial Mechanics, as provided by high-level scientists working in this field. It covers theoretical investigations as well as applications to concrete problems. Outstanding review papers are included in the book and they introduce the reader to leading subjects, like the variational approaches to find periodic orbits and the space debris polluting the circumterrestrial space.

Author : Zdzislaw Musielak
Publisher : Springer
ISBN 13 : 3319582267
Total Pages : 109 pages
Book Rating : 4.69/5 ( download)

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Download or read book Three Body Dynamics and Its Applications to Exoplanets written by Zdzislaw Musielak and published by Springer. This book was released on 2017-07-22 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief book provides an overview of the gravitational orbital evolution of few-body systems, in particular those consisting of three bodies. The authors present the historical context that begins with the origin of the problem as defined by Newton, which was followed up by Euler, Lagrange, Laplace, and many others. Additionally, they consider the modern works from the 20th and 21st centuries that describe the development of powerful analytical methods by Poincare and others. The development of numerical tools, including modern symplectic methods, are presented as they pertain to the identification of short-term chaos and long term integrations of the orbits of many astronomical architectures such as stellar triples, planets in binaries, and single stars that host multiple exoplanets. The book includes some of the latest discoveries from the Kepler and now K2 missions, as well as applications to exoplanets discovered via the radial velocity method. Specifically, the authors give a unique perspective in relation to the discovery of planets in binary star systems and the current search for extrasolar moons.

Author : V.V. Beletsky
Publisher : Birkhäuser
ISBN 13 : 3034883609
Total Pages : 382 pages
Book Rating : 4.03/5 ( download)

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Download or read book Essays on the Motion of Celestial Bodies written by V.V. Beletsky and published by Birkhäuser. This book was released on 2012-12-06 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interesting and often unexpected achievements of the mechanics of space flight throw a new light onto several classical problems. The book’s emphasis is on analysis carried out on the level of graphs and drawings, and sometimes numbers, revealing the beauty of the research process leading to the results.