Generating Families In The Restricted Three Body Problem
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Generating Families in the Restricted Three Body Problem
Author | : Michel Henon |
Publsiher | : Springer Science & Business Media |
Total Pages | : 308 |
Release | : 2001-04-24 |
Genre | : Language Arts & Disciplines |
ISBN | : 9783540417330 |
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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.
Generating Families in the Restricted Three Body Problem
Author | : Michel Henon |
Publsiher | : Springer |
Total Pages | : 296 |
Release | : 2014-01-15 |
Genre | : Electronic Book |
ISBN | : 3662141558 |
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Generating Families in the Restricted Three Body Problem
Author | : Michel Henon |
Publsiher | : Springer Science & Business Media |
Total Pages | : 280 |
Release | : 2003-07-01 |
Genre | : Science |
ISBN | : 9783540696506 |
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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.
Generating Families in the Restricted Three Body Problem
Author | : Michel Henon |
Publsiher | : Springer Science & Business Media |
Total Pages | : 304 |
Release | : 2003-07-01 |
Genre | : Science |
ISBN | : 9783540447122 |
Download Generating Families in the Restricted Three Body Problem Book in PDF, Epub and Kindle
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.
The Restricted 3 Body Problem Plane Periodic Orbits
Author | : Alexander D. Bruno |
Publsiher | : Walter de Gruyter |
Total Pages | : 377 |
Release | : 2011-05-03 |
Genre | : Mathematics |
ISBN | : 9783110901733 |
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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
Periodic Orbits in the Elliptic Restricted Three body Problem
Author | : R. A. Broucke |
Publsiher | : Unknown |
Total Pages | : 144 |
Release | : 1969 |
Genre | : Artificial satellites |
ISBN | : UOM:39015040397435 |
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Periodic Quasi Periodic and Chaotic Motions in Celestial Mechanics Theory and Applications
Author | : Alessandra Celletti,Sylvio Ferraz-Mello |
Publsiher | : Springer Science & Business Media |
Total Pages | : 434 |
Release | : 2007-02-02 |
Genre | : Science |
ISBN | : 9781402053252 |
Download Periodic Quasi Periodic and Chaotic Motions in Celestial Mechanics Theory and Applications Book in PDF, Epub and Kindle
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.
Three Body Dynamics and Its Applications to Exoplanets
Author | : Zdzislaw Musielak,Billy Quarles |
Publsiher | : Springer |
Total Pages | : 109 |
Release | : 2017-07-22 |
Genre | : Science |
ISBN | : 9783319582269 |
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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.