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Generating Families In The Restricted Three Body Problem

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Generating Families In The Restricted Three Body Problem

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Author : Michel Henon
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-01

Generating Families In The Restricted Three Body Problem written by Michel Henon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Science categories.

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

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Author : Michel Henon
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-04-24

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

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Author : Michel Henon
language : en
Publisher: Springer
Release Date : 2014-01-15

Generating Families In The Restricted Three Body Problem written by Michel Henon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

The Restricted 3 Body Problem Plane Periodic Orbits

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Author : Alexander D. Bruno
language : en
Publisher: Walter de Gruyter
Release Date : 2011-05-03

The Restricted 3 Body Problem Plane Periodic Orbits written by Alexander D. Bruno and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-03 with Mathematics categories.

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

Generating Families In The Restricted Three Body Problem

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Author : Michel Henon
language : en
Publisher: Springer
Release Date : 2014-01-15

Three Body Dynamics And Its Applications To Exoplanets

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Author : Zdzislaw Musielak
language : en
Publisher: Springer
Release Date : 2017-07-22

Three Body Dynamics And Its Applications To Exoplanets written by Zdzislaw Musielak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-22 with Science categories.

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.

Dynamical Systems

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Author : Wang Sang Koon
language : en
Publisher: Springer
Release Date : 2011-06-01

Dynamical Systems written by Wang Sang Koon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-01 with Mathematics categories.

This book considers global solutions to the restricted three-body problem from a geometric point of view. The authors seek dynamical channels in the phase space which wind around the planets and moons and naturally connect them. These low energy passageways could slash the amount of fuel spacecraft need to explore and develop our solar system. In order to effectively exploit these passageways, the book addresses the global transport. It goes beyond the traditional scope of libration point mission design, developing tools for the design of trajectories which take full advantage of natural three or more body dynamics, thereby saving precious fuel and gaining flexibility in mission planning. This is the key for the development of some NASA mission trajectories, such as low energy libration point orbit missions (e.g., the sample return Genesis Discovery Mission), low energy lunar missions and low energy tours of outer planet moon systems, such as a mission to tour and explore in detail the icy moons of Jupiter. This book can serve as a valuable resource for graduate students and advanced undergraduates in applied mathematics and aerospace engineering, as well as a manual for practitioners who work on libration point and deep space missions in industry and at government laboratories. the authors include a wealth of background material, but also bring the reader up to a portion of the research frontier.

The Three Body Problem

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Author : Mauri J. Valtonen
language : en
Publisher: Cambridge University Press
Release Date : 2006-03-02

The Three Body Problem written by Mauri J. Valtonen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-02 with Mathematics categories.

This book surveys statistical and perturbation methods for the solution of the general three body problem.

Periodic Quasi Periodic And Chaotic Motions In Celestial Mechanics Theory And Applications

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Author : Alessandra Celletti
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-02

Periodic Quasi Periodic And Chaotic Motions In Celestial Mechanics Theory And Applications written by Alessandra Celletti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-02 with Science categories.

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.

Dynamics Games And Science I

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Author : Mauricio Matos Peixoto
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-29

Dynamics Games And Science I written by Mauricio Matos Peixoto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-29 with Mathematics categories.

Dynamics, Games and Science I and II are a selection of surveys and research articles written by leading researchers in mathematics. The majority of the contributions are on dynamical systems and game theory, focusing either on fundamental and theoretical developments or on applications to modeling in biology, ecomonics, engineering, finances and psychology. The papers are based on talks given at the International Conference DYNA 2008, held in honor of Mauricio Peixoto and David Rand at the University of Braga, Portugal, on September 8-12, 2008. The aim of these volumes is to present cutting-edge research in these areas to encourage graduate students and researchers in mathematics and other fields to develop them further.

Generating Families In The Restricted Three Body Problem

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