Periodic Solutions of the Restricted Three Body Problem Representing Analytic Continuations of Keplerian Elliptic Motions

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ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Periodic Solutions of the Restricted Three Body Problem Representing Analytic Continuations of Keplerian Elliptic Motions by : Richard F. Arenstorf

Download or read book Periodic Solutions of the Restricted Three Body Problem Representing Analytic Continuations of Keplerian Elliptic Motions written by Richard F. Arenstorf and published by . This book was released on 1963 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

NASA Technical Note

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Publisher :
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis NASA Technical Note by :

Download or read book NASA Technical Note written by and published by . This book was released on 1963 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Restricted 3-Body Problem: Plane Periodic Orbits

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Publisher : Walter de Gruyter
ISBN 13 : 3110901730
Total Pages : 377 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis The Restricted 3-Body Problem: Plane Periodic Orbits by : Alexander D. Bruno

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

Trajectories of Artificial Celestial Bodies as Determined from Observations / Trajectoires des Corps Celestes Artificiels Déterminées D’après les Observations

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Publisher : Springer Science & Business Media
ISBN 13 : 3642493262
Total Pages : 282 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Trajectories of Artificial Celestial Bodies as Determined from Observations / Trajectoires des Corps Celestes Artificiels Déterminées D’après les Observations by : J. Kovalevsky

Download or read book Trajectories of Artificial Celestial Bodies as Determined from Observations / Trajectoires des Corps Celestes Artificiels Déterminées D’après les Observations written by J. Kovalevsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: In May 1962 the International Union of Theoretical and Applied Mechanics (IUTAM) organized a symposium in Paris on the theory of the movement of the Earth's artificial satellites designated to confront the results of the first spatial experiences with the mechanical point of view. The papers submitted during this meeting have been published in 1963 in a collection entitled "Dynamics of Satellites" by Springer Verlag. During the last three years the importance of studies pertaining to the dynamics of artificial satellites has continued to increase, and many results due to observations have led to a deeper knowledge of the field of forces in which these objects move, particularly the field of gravitation of the Earth, the forces due to pressure of radiation, friction of the atmosphere, etc . . . A new symposium seemed therefore suitable to determine these recent advances. However, this time it appeared appropriate to consider it more from the point of view of the interpretation obtained from the results of observations (determination of orbits and forces existing) than from the point of view of the theory of motion. For this reason the complete title of the second symposium is as follows: "Trajectories of Artificial Celestial Bodies, as Determined from Observations".

Generating Families in the Restricted Three-Body Problem

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Publisher : Springer Science & Business Media
ISBN 13 : 3540638024
Total Pages : 282 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Generating Families in the Restricted Three-Body Problem by : Michel Henon

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 1997-11-27 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical three-body problem is of great 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. Here the author explains and organizes 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. Many cases are distinguished and studied separately and detailed recipies are given. Their use is illustrated by determining generating families, and comparing them with numerical computations for the Earth+Moon and Sun-Jupiter systems.

The Three-Body Problem

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Publisher : Elsevier
ISBN 13 : 0444600744
Total Pages : 593 pages
Book Rating : 4.4/5 (446 download)

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Book Synopsis The Three-Body Problem by : C. Marchal

Download or read book The Three-Body Problem written by C. Marchal and published by Elsevier. This book was released on 2012-12-02 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent research on the theory of perturbations, the analytical approach and the quantitative analysis of the three-body problem have reached a high degree of perfection. The use of electronics has aided developments in quantitative analysis and has helped to disclose the extreme complexity of the set of solutions. This accelerated progress has given new orientation and impetus to the qualitative analysis that is so complementary to the quantitative analysis. The book begins with the various formulations of the three-body problem, the main classical results and the important questions and conjectures involved in this subject. The main part of the book describes the remarkable progress achieved in qualitative analysis which has shed new light on the three-body problem. It deals with questions such as escapes, captures, periodic orbits, stability, chaotic motions, Arnold diffusion, etc. The most recent tests of escape have yielded very impressive results and border very close on the true limits of escape, showing the domain of bounded motions to be much smaller than was expected. An entirely new picture of the three-body problem is emerging, and the book reports on this recent progress. The structure of the solutions for the three-body problem lead to a general conjecture governing the picture of solutions for all Hamiltonian problems. The periodic, quasi-periodic and almost-periodic solutions form the basis for the set of solutions and separate the chaotic solutions from the open solutions.

Theory of Orbit

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Publisher : Elsevier
ISBN 13 : 0323143466
Total Pages : 684 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Theory of Orbit by : Victory Szebehely

Download or read book Theory of Orbit written by Victory Szebehely and published by Elsevier. This book was released on 2012-12-02 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

NASA Technical Memorandum

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Publisher :
ISBN 13 :
Total Pages : 48 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis NASA Technical Memorandum by :

Download or read book NASA Technical Memorandum written by and published by . This book was released on 1963 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Hamiltonian Dynamical Systems and the N-Body Problem

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Publisher : Springer Science & Business Media
ISBN 13 : 1475740735
Total Pages : 304 pages
Book Rating : 4.4/5 (757 download)

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

Download or read book Introduction to Hamiltonian Dynamical Systems and the N-Body Problem written by Kenneth Meyer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Hamiltonian systems is a vast subject which can be studied from many different viewpoints. This book develops the basic theory of Hamiltonian differential equations from a dynamical systems point of view. That is, the solutions of the differential equations are thought of as curves in a phase space and it is the geometry of these curves that is the important object of study. The analytic underpinnings of the subject are developed in detail. The last chapter on twist maps has a more geometric flavor. It was written by Glen R. Hall. The main example developed in the text is the classical N-body problem, i.e., the Hamiltonian system of differential equations which describe the motion of N point masses moving under the influence of their mutual gravitational attraction. Many of the general concepts are applied to this example. But this is not a book about the N-body problem for its own sake. The N-body problem is a subject in its own right which would require a sizable volume of its own. Very few of the special results which only apply to the N-body problem are given.

Scientific and Technical Aerospace Reports

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ISBN 13 :
Total Pages : 196 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1963 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

NASA Scientific and Technical Reports

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ISBN 13 :
Total Pages : 260 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis NASA Scientific and Technical Reports by : United States. National Aeronautics and Space Administration Scientific and Technical Information Division

Download or read book NASA Scientific and Technical Reports written by United States. National Aeronautics and Space Administration Scientific and Technical Information Division and published by . This book was released on 1964 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Selected Listing of NASA Scientific and Technical Reports for ...

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Publisher :
ISBN 13 :
Total Pages : 258 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis A Selected Listing of NASA Scientific and Technical Reports for ... by : United States. National Aeronautics and Space Administration. Scientific and Technical Information Division

Download or read book A Selected Listing of NASA Scientific and Technical Reports for ... written by United States. National Aeronautics and Space Administration. Scientific and Technical Information Division and published by . This book was released on 1963 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Restricted Three-Body Problem and Holomorphic Curves

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Publisher : Springer
ISBN 13 : 3319722786
Total Pages : 374 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis The Restricted Three-Body Problem and Holomorphic Curves by : Urs Frauenfelder

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

Applied Mechanics Reviews

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Publisher :
ISBN 13 :
Total Pages : 542 pages
Book Rating : 4.:/5 (26 download)

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Book Synopsis Applied Mechanics Reviews by :

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1972 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:

NASA Technical Note

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Publisher :
ISBN 13 :
Total Pages : 362 pages
Book Rating : 4.:/5 (35 download)

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Book Synopsis NASA Technical Note by :

Download or read book NASA Technical Note written by and published by . This book was released on with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ordinary Differential Equations

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Publisher : Elsevier
ISBN 13 : 1483270114
Total Pages : 622 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Ordinary Differential Equations by : Leonard Weiss

Download or read book Ordinary Differential Equations written by Leonard Weiss and published by Elsevier. This book was released on 2014-05-10 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary Differential Equations: 1971 NRL–MRC Conference provides information pertinent to the fundamental aspects of ordinary differential equations. This book covers a variety of topics, including geometric and qualitative theory, analytic theory, functional differential equation, dynamical systems, and algebraic theory. Organized into two parts encompassing 51 chapters, this book begins with an overview of the results on the existence of periodic solutions of a differential equation. This text then describes an index for the isolated invariant sets of a flow on a compact metric space, which contains exactly the information of the Morse index. Other chapters consider the studies of certain classes of equations that can be interpreted as models of biological or economic processes. This book discusses as well the absolute stability of some classes of integro-differential systems. The final chapter deals with first-order differential equations. This book is a valuable resource for mathematicians, graduate students, and research workers.

Solving Differential Equations in R

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Publisher : Springer Science & Business Media
ISBN 13 : 3642280706
Total Pages : 248 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Solving Differential Equations in R by : Karline Soetaert

Download or read book Solving Differential Equations in R written by Karline Soetaert and published by Springer Science & Business Media. This book was released on 2012-06-06 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R for solving differential equations. However, it has been our goal that non-mathematicians should at least understand the basics of the methods, while obtaining entrance into the relevant literature that provides more mathematical background. Therefore, each chapter that deals with R examples is preceded by a chapter where the theory behind the numerical methods being used is introduced. In the sections that deal with the use of R for solving differential equations, we have taken examples from a variety of disciplines, including biology, chemistry, physics, pharmacokinetics. Many examples are well-known test examples, used frequently in the field of numerical analysis.