Periodic Solutions Of The N Body Problem

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Periodic Solutions of the N-Body Problem

Author : Kenneth R. Meyer
Publisher : Springer
ISBN 13 : 3540480730
Total Pages : 149 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Periodic Solutions of the N-Body Problem by : Kenneth R. Meyer

Download or read book Periodic Solutions of the N-Body Problem written by Kenneth R. Meyer and published by Springer. This book was released on 2006-11-17 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The N-body problem is the classical prototype of a Hamiltonian system with a large symmetry group and many first integrals. These lecture notes are an introduction to the theory of periodic solutions of such Hamiltonian systems. From a generic point of view the N-body problem is highly degenerate. It is invariant under the symmetry group of Euclidean motions and admits linear momentum, angular momentum and energy as integrals. Therefore, the integrals and symmetries must be confronted head on, which leads to the definition of the reduced space where all the known integrals and symmetries have been eliminated. It is on the reduced space that one can hope for a nonsingular Jacobian without imposing extra symmetries. These lecture notes are intended for graduate students and researchers in mathematics or celestial mechanics with some knowledge of the theory of ODE or dynamical system theory. The first six chapters develops the theory of Hamiltonian systems, symplectic transformations and coordinates, periodic solutions and their multipliers, symplectic scaling, the reduced space etc. The remaining six chapters contain theorems which establish the existence of periodic solutions of the N-body problem on the reduced space.

Periodic Solutions of the N-Body Problem

Author : Kenneth R. Meyer
Publisher : Springer Science & Business Media
ISBN 13 : 9783540666301
Total Pages : 172 pages
Book Rating : 4.6/5 (663 download)

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Book Synopsis Periodic Solutions of the N-Body Problem by : Kenneth R. Meyer

Download or read book Periodic Solutions of the N-Body Problem written by Kenneth R. Meyer and published by Springer Science & Business Media. This book was released on 1999-11-17 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lecture Notes in Mathematics This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes 1. Research monographs 2. Lectures on a new field or presentations of a new angle in a classical field 3. Summer schools and intensive courses on topics of current research Texts which are out of print but still in demand may also be considered. The timeliness of a manuscript is sometimes more important than its form, which might be preliminary or tentative. Details of the editorial policy can be found on the inside front-cover of a current volume. Manuscripts should be submitted in camera-ready form according to Springer-Verlag's specification: technical instructions will be sent on request. TEX macros may be found at: http://www.springer.de/math/authors/b-tex.html Select the version of TEX you use and then click on "Monographs". A subject index should be included. We recommend contacting the publisher or the series editors at an early stage of your project. Addresses are given on the inside back-cover.

Introduction to Hamiltonian Dynamical Systems and the N-Body Problem

Author : Kenneth R. Meyer
Publisher : Springer
ISBN 13 : 3319536915
Total Pages : 389 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by : Kenneth R. Meyer

Download or read book Introduction to Hamiltonian Dynamical Systems and the N-Body Problem written by Kenneth R. Meyer and published by Springer. This book was released on 2017-05-04 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. ... It is a well-organized and accessible introduction to the subject ... . This is an attractive book ... ." (William J. Satzer, The Mathematical Association of America, March, 2009) “The second edition of this text infuses new mathematical substance and relevance into an already modern classic ... and is sure to excite future generations of readers. ... This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. ... it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.” (Marian Gidea, Mathematical Reviews, Issue 2010 d)

European Congress of Mathematics

Author : Carles Casacuberta
Publisher : Birkhäuser
ISBN 13 : 3034882661
Total Pages : 630 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis European Congress of Mathematics by : Carles Casacuberta

Download or read book European Congress of Mathematics written by Carles Casacuberta and published by Birkhäuser. This book was released on 2012-12-06 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.

KAM Stability and Celestial Mechanics

Author : Alessandra Celletti
Publisher : American Mathematical Soc.
ISBN 13 : 0821841696
Total Pages : 150 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis KAM Stability and Celestial Mechanics by : Alessandra Celletti

Download or read book KAM Stability and Celestial Mechanics written by Alessandra Celletti and published by American Mathematical Soc.. This book was released on 2007 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The authors consider the Restricted, Circular, Planar, Three-Body Problem (RCP3BP), i.e., the problem of studying the planar motions of a small body subject to the gravitational attraction of two primary bodies revolving on circular Keplerian orbits (which are assumed not to be influenced by the small body). When the mass ratio of the two primary bodies is small, the RCP3BP is described by a nearly-integrable Hamiltonian system with two degrees of freedom; in a region of phase space corresponding to nearly elliptical motions with non-small eccentricities, the system is well described by Delaunay variables. The Sun-Jupiter observed motion is nearly circular and an asteroid of the Asteroidal belt may be assumed not to influence the Sun-Jupiter motion. The Jupiter-Sun mass ratio is slightly less than 1/1000. The authors consider the motion of the asteroid 12 Victoria taking into account only the Sun-Jupiter gravitational attraction regarding such a system as a prototype of a RCP3BP. for values of mass ratios up to 1/1000, they prove the existence of two-dimensional KAM tori on a fixed three-dimensional energy level corresponding to the observed energy of the Sun-Jupiter-Victoria system. Such tori trap the evolution of phase points ``close'' to the observed physical data of the Sun-Jupiter-Victoria system. As a consequence, in the RCP3BP description, the motion of Victoria is proven to be forever close to an elliptical motion. The proof is based on: 1) a new iso-energetic KAM theory; 2) an algorithm for computing iso-energetic, approximate Lindstedt series; 3) a computer-aided application of 1)+2) to the Sun-Jupiter-Victoria system. The paper is self-contained but does not include the ($\sim$ 12000 lines) computer programs, which may be obtained by sending an e-mail to one of the authors.

Lectures on Celestial Mechanics

Author : Carl L. Siegel
Publisher : Springer Science & Business Media
ISBN 13 : 9783540586562
Total Pages : 312 pages
Book Rating : 4.5/5 (865 download)

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Book Synopsis Lectures on Celestial Mechanics by : Carl L. Siegel

Download or read book Lectures on Celestial Mechanics written by Carl L. Siegel and published by Springer Science & Business Media. This book was released on 1995-02-15 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book represents to a large extent the translation of the German "Vorlesungen über Himmelsmechanik" by C. L. Siegel. The demand for a new edition and for an English translation gave rise to the present volume which, however, goes beyond a mere translation. To take account of recent work in this field a number of sections have been added, especially in the third chapter which deals with the stability theory. Still, it has not been attempted to give a complete presentation of the subject, and the basic prganization of Siegel's original book has not been altered. The emphasis lies in the development of results and analytic methods which are based on the ideas of H. Poincare, G. D. Birkhoff, A. Liapunov and, as far as Chapter I is concerned, on the work of K. F. Sundman and C. L. Siegel. In recent years the measure-theoretical aspects of mechanics have been revitalized and have led to new results which will not be discussed here. In this connection we refer, in particular, to the interesting book by V. I. Arnold and A. Avez on "Problemes Ergodiques de la Mecanique Classique", which stresses the interaction of ergodic theory and mechanics. We list the points in which the present book differs from the German text. In the first chapter two sections on the tri pie collision in the three body problem have been added by C. L. Siegel.

Numerical Continuation Methods for Dynamical Systems

Author : Bernd Krauskopf
Publisher : Springer
ISBN 13 : 1402063563
Total Pages : 411 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Numerical Continuation Methods for Dynamical Systems by : Bernd Krauskopf

Download or read book Numerical Continuation Methods for Dynamical Systems written by Bernd Krauskopf and published by Springer. This book was released on 2007-11-06 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.

Mathematics of Complexity and Dynamical Systems

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
ISBN 13 : 1461418054
Total Pages : 1885 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Mathematics of Complexity and Dynamical Systems by : Robert A. Meyers

Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Nonlinear Analysis and Continuum Mechanics

Author : Giuseppe Butazzo
Publisher : Springer Science & Business Media
ISBN 13 : 146122196X
Total Pages : 149 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Nonlinear Analysis and Continuum Mechanics by : Giuseppe Butazzo

Download or read book Nonlinear Analysis and Continuum Mechanics written by Giuseppe Butazzo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The chapters in this volume deal with four fields with deep historical roots that remain active areas reasearch: partial differential equations, variational methods, fluid mechanics, and thermodynamics. The collection is intended to serve two purposes: First, to honor James Serrin, in whose work the four fields frequently interacted; and second, to bring together work in fields that are usually pursued independently but that remain remarkably interrelated. Serrin's contributions to mathematical analysis and its applications are fundamental and include such theorems and methods as the Gilbarg- Serrin theorem on isoated singularities, the Serrin symmetry theorem, the Alexandrov-Serrin moving-plane technique, The Peletier-Serrin uniqueness theorem, and the Serrin integal of the calculus of variations. Serrin has also been noted for the elegance of his mathematical work and for the effectiveness of his teaching and collaborations.

Perturbation Theory

Author : Giuseppe Gaeta
Publisher : Springer Nature
ISBN 13 : 1071626213
Total Pages : 601 pages
Book Rating : 4.0/5 (716 download)

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Book Synopsis Perturbation Theory by : Giuseppe Gaeta

Download or read book Perturbation Theory written by Giuseppe Gaeta and published by Springer Nature. This book was released on 2022-12-16 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.

The Three-Body Problem and the Equations of Dynamics

Author : Henri Poincaré
Publisher : Springer
ISBN 13 : 3319528998
Total Pages : 265 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis The Three-Body Problem and the Equations of Dynamics by : Henri Poincaré

Download or read book The Three-Body Problem and the Equations of Dynamics written by Henri Poincaré and published by Springer. This book was released on 2017-05-11 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations’ solutions, such as orbital resonances and horseshoe orbits. Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating.

Celestial Mechanics

Author : Donald Saari
Publisher : American Mathematical Soc.
ISBN 13 : 0821829025
Total Pages : 282 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Celestial Mechanics by : Donald Saari

Download or read book Celestial Mechanics written by Donald Saari and published by American Mathematical Soc.. This book was released on 2002 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the proceedings from an international conference on celestial mechanics held at Northwestern University (Evanston, IL) in celebration of Donald Saari's sixtieth birthday. Many leading experts and researchers presented their recent results. Don Saari's significant contribution to the field came in the late 1960s through a series of important works. His work revived the singularity theory in the $n$-body problem which was started by Poincare and Painleve. Saari'ssolution of the Littlewood conjecture, his work on singularities, collision and noncollision, on central configurations, his decompositions of configurational velocities, etc., are still much studied today and were reflected throughout the conference. This volume covers various topics of currentresearch, from central configurations to stability of periodic orbits, from variational methods to diffusion mechanisms, from the dynamics of secular systems to global dynamics of the solar systems via frequency analysis, from Hill's problem to the low energy transfer orbits and mission design in space travel, and more. This classic field of study is very much alive today and this volume offers a comprehensive representation of the latest research results.

Libration Point Orbits and Applications

Author : Gerard G¢mez
Publisher : World Scientific
ISBN 13 : 9812383638
Total Pages : 695 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Libration Point Orbits and Applications by : Gerard G¢mez

Download or read book Libration Point Orbits and Applications written by Gerard G¢mez and published by World Scientific. This book was released on 2003 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state of the art in numerical and analytical techniques as well as future trends associated with mission design for libration point orbits. It contains papers explaining theoretical developments and their applications, including the accurate description of some actual libration point missions of ESA and NASA. The existing software in the field and some applications beyond the neighborhood of the Earth are also presented. Special emphasis is placed on the use of dynamical systems methodology in the libration-point-orbits mission design.

New Methods of Celestial Mechanics

Author : Henri Poincaré
Publisher :
ISBN 13 :
Total Pages : 352 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis New Methods of Celestial Mechanics by : Henri Poincaré

Download or read book New Methods of Celestial Mechanics written by Henri Poincaré and published by . This book was released on 1967 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Theory of Orbits, the Restricted Problem of Three Bodies

Author : Victor G. Szebehely
Publisher :
ISBN 13 :
Total Pages : 684 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Theory of Orbits, the Restricted Problem of Three Bodies by : Victor G. Szebehely

Download or read book Theory of Orbits, the Restricted Problem of Three Bodies written by Victor G. Szebehely and published by . This book was released on 1967 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: Descripción del editor: "Theory of Orbits: The Restricted Problem of Three Bodies is a 10-chapter text that covers the significance of the restricted problem of three bodies in analytical dynamics, celestial mechanics, and space dynamics. The introductory part looks into the use of three essentially different approaches to dynamics, namely, the qualitative, the quantitative, and the formalistic. The opening chapters consider the formulation of equations of motion in inertial and in rotating coordinate systems, as well as the reductions of the problem of three bodies and the corresponding streamline analogies. These topics are followed by discussions on the regularization and writing of equations of motion in a singularity-free systems; the principal qualitative aspect of the restricted problem of the curves of zero velocity; and the motion and nonlinear stability in the neighborhood of libration points. This text further explores the principles of Hamiltonian dynamics and its application to the restricted problem in the extended phase space. A chapter treats the problem of two bodies in a rotating coordinate system and treats periodic orbits in the restricted problem. Another chapter focuses on the comparison of the lunar and interplanetary orbits in the Soviet and American literature. The concluding chapter is devoted to modifications of the restricted problem, such as the elliptic, three-dimensional, and Hill's problem. This book is an invaluable source for astronomers, engineers, and mathematicians ". Academic Press.

Xivth International Congress On Mathematical Physics

Author : Jean-claude Zambrini
Publisher : World Scientific
ISBN 13 : 9814480762
Total Pages : 718 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Xivth International Congress On Mathematical Physics by : Jean-claude Zambrini

Download or read book Xivth International Congress On Mathematical Physics written by Jean-claude Zambrini and published by World Scientific. This book was released on 2006-03-07 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2003 the XIV International Congress on Mathematical Physics (ICMP) was held in Lisbon with more than 500 participants. Twelve plenary talks were given in various fields of Mathematical Physics: E Carlen «On the relation between the Master equation and the Boltzmann Equation in Kinetic Theory»; A Chenciner «Symmetries and “simple” solutions of the classical n-body problem»; M J Esteban «Relativistic models in atomic and molecular physics»; K Fredenhagen «Locally covariant quantum field theory»; K Gawedzki «Simple models of turbulent transport»; I Krichever «Algebraic versus Liouville integrability of the soliton systems»; R V Moody «Long-range order and diffraction in mathematical quasicrystals»; S Smirnov «Critical percolation and conformal invariance»; J P Solovej «The energy of charged matter»; V Schomerus «Strings through the microscope»; C Villani «Entropy production and convergence to equilibrium for the Boltzmann equation»; D Voiculescu «Aspects of free probability».The book collects as well carefully selected invited Session Talks in: Dynamical Systems, Integrable Systems and Random Matrix Theory, Condensed Matter Physics, Equilibrium Statistical Mechanics, Quantum Field Theory, Operator Algebras and Quantum Information, String and M Theory, Fluid Dynamics and Nonlinear PDE, General Relativity, Nonequilibrium Statistical Mechanics, Quantum Mechanics and Spectral Theory, Path Integrals and Stochastic Analysis.

Dynamical Systems

Author : Wang Sang Koon
Publisher : Springer
ISBN 13 : 9780387495156
Total Pages : 336 pages
Book Rating : 4.4/5 (951 download)

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Book Synopsis Dynamical Systems by : Wang Sang Koon

Download or read book Dynamical Systems written by Wang Sang Koon and published by Springer. This book was released on 2011-06-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.