Analytical Techniques Of Celestial Mechanics

Author : Victor A. Brumberg
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642794544

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Analytical Techniques of Celestial Mechanics by Victor A. Brumberg Pdf

The aim of this book is to describe contemporary analytical and semi analytical techniques for solving typical celestial-mechanics problems. The word "techniques" is used here as a term intermediate between "methods" and "recipes". One often conceives some method of solution of a problem as a general mathematical tool, while not taking much care with its computa tional realization. On the other hand, the word "recipes" may nowadays be understood in the sense of the well-known book Numerical Recipes (Press et al. , 1992), where it means both algorithms and their specific program realiza tion in Fortran, C or Pascal. Analytical recipes imply the use of some general or specialized computer algebra system (CAS). The number of different CAS currently employed in celestial mechanics is too large to specify just a few of the most preferable systems. Besides, it seems reasonable not to mix the essence of any algorithm with its particular program implementation. For these reasons, the analytical techniques of this book are to be regarded as algorithms to be implemented in different ways depending on the hardware and software available. The book was preceded by Analytical Algorithms of Celestial Mechanics by the same author, published in Russian in 1980. In spite of there being much common between these books, the present one is in fact a new mono graph.

Author : Victor Brumberg
Publisher : Springer
Page : 236 pages
File Size : 40,6 Mb
Release : 2011-12-22
Category : Science
ISBN : 3642794556

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Analytical Techniques of Celestial Mechanics by Victor Brumberg Pdf

The aim of this book is to describe contemporary analytical and semi analytical techniques for solving typical celestial-mechanics problems. The word "techniques" is used here as a term intermediate between "methods" and "recipes". One often conceives some method of solution of a problem as a general mathematical tool, while not taking much care with its computa tional realization. On the other hand, the word "recipes" may nowadays be understood in the sense of the well-known book Numerical Recipes (Press et al. , 1992), where it means both algorithms and their specific program realiza tion in Fortran, C or Pascal. Analytical recipes imply the use of some general or specialized computer algebra system (CAS). The number of different CAS currently employed in celestial mechanics is too large to specify just a few of the most preferable systems. Besides, it seems reasonable not to mix the essence of any algorithm with its particular program implementation. For these reasons, the analytical techniques of this book are to be regarded as algorithms to be implemented in different ways depending on the hardware and software available. The book was preceded by Analytical Algorithms of Celestial Mechanics by the same author, published in Russian in 1980. In spite of there being much common between these books, the present one is in fact a new mono graph.

Author : Gleb Aleksandrovich Chebotarev
Publisher : Unknown
Page : 362 pages
File Size : 52,7 Mb
Release : 1967
Category : Science
ISBN : UOM:39015008084579

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Analytical and Numerical Methods of Celestial Mechanics by Gleb Aleksandrovich Chebotarev Pdf

The stated purpose of this book is to fill a gap in the Russian-language astronomical literature, which had lacked a fundamental textbook on celestial mechanics. The treatment is limited to detailed step-by-step analysis of six methods on which present-day theories of planetary, cometary, and satellite motion are based, beginning with the differential equations and culminating in a comparison of theory with observations. These are the Laplace-Newcomb method, the Hill planetary method, the method of variation of arbitrary constants, the Hill lunar method, and the periodic-orbit and Cowell methods. (Author).

Author : Aurel Wintner
Publisher : Unknown
Page : 472 pages
File Size : 50,6 Mb
Release : 1941
Category : Science
ISBN : UOM:39015002003864

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The Analytical Foundations of Celestial Mechanics by Aurel Wintner Pdf

Author : Forest Ray Moulton
Publisher : Unknown
Page : 478 pages
File Size : 46,7 Mb
Release : 1914
Category : Science
ISBN : STANFORD:36105046458993

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An Introduction to Celestial Mechanics by Forest Ray Moulton Pdf

Author : Forest Ray Moulton
Publisher : Courier Corporation
Page : 450 pages
File Size : 47,9 Mb
Release : 2012-04-26
Category : Science
ISBN : 9780486140681

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An Introduction to Celestial Mechanics by Forest Ray Moulton Pdf

An unrivaled text in the field of celestial mechanics, Moulton's theoretical work on the prediction and interpretation of celestial phenomena has not been superseded. By providing a general account of all parts of celestial mechanics without an over-full treatment of any single aspect, by stating all the problems in advance, and, where the transformations are long, giving an outline of the steps which must be made, and by noting all the places where assumptions have been introduced or unjustified methods employed, Moulton has insured that his work will be valuable to all who are interested in the subject. The text is divided into ten chapters which progress logically in terms of the difficulty of their subject matter. They are: Fundamental Principles and Definitions, Rectilinear Motion, Central Forces, The Potential and Attractions of Bodies, The Problem of Two Bodies, The Determination of Orbits, The General Integrals of the Problem of n Bodies, The Problem of Three Bodies, Perturbations ― Geometrical Considerations, and Perturbations ― Analytical Method. Important topics cove red include general equations, motion of falling particles, the heat of the sun, simultaneous differential equations, examples where J is a function of the coordinates alone, the universality of Newton's law, determination of the orbit from the law of force, attractions of simple solids, potential and attractions of simple bodies and ellipsoids, Ivory's method and level surfaces, elements of orbits, expansions and positions in orbits, transformations of coordinates, the Laplacian and Gaussian methods of determining orbits, motion of center of mass and area integrals, motion of the infinitesimal body, surfaces of zero relative velocity, effects of the components of the disturbing force, lunar theory, method of computing perturbations, and the perturbative function. Each chapter is followed by a historical sketch and bibliography pertaining to that subject. Over 200 problems appear at key points in the text, many of them answered.

Author : Gerhard Beutler
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 51,9 Mb
Release : 2005-11-20
Category : Science
ISBN : 9783540268703

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Methods of Celestial Mechanics by Gerhard Beutler Pdf

G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students as well as an excellent reference for practitioners. The first volume gives a thorough treatment of celestial mechanics and presents all the necessary mathematical details that a professional would need. The reader will appreciate the well-written chapters on numerical solution techniques for ordinary differential equations, as well as that on orbit determination. In the second volume applications to the rotation of earth and moon, to artificial earth satellites and to the planetary system are presented. The author addresses all aspects that are of importance in high-tech applications, such as the detailed gravitational fields of all planets and the earth, the oblateness of the earth, the radiation pressure and the atmospheric drag. The concluding part of this monumental treatise explains and details state-of-the-art professional and thoroughly-tested software for celestial mechanics.

Author : Gerhard Beutler
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 50,9 Mb
Release : 2005-11-21
Category : Science
ISBN : 9783540265122

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Methods of Celestial Mechanics by Gerhard Beutler Pdf

G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students as well as an excellent reference for practitioners. The first volume gives a thorough treatment of celestial mechanics and presents all the necessary mathematical details that a professional would need. The reader will appreciate the well-written chapters on numerical solution techniques for ordinary differential equations, as well as that on orbit determination. In the second volume applications to the rotation of earth and moon, to artificial earth satellites and to the planetary system are presented. The author addresses all aspects that are of importance in high-tech applications, such as the detailed gravitational fields of all planets and the earth, the oblateness of the earth, the radiation pressure and the atmospheric drag. The concluding part of this monumental treatise explains and details state-of-the-art professional and thoroughly-tested software for celestial mechanics.

Author : Gerhard Beutler
Publisher : Springer
Page : 466 pages
File Size : 49,6 Mb
Release : 2009-09-02
Category : Science
ISBN : 3540829172

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Methods of Celestial Mechanics by Gerhard Beutler Pdf

G. Beutler's Methods of Celestial Mechanics is a coherent textbook for students as well as an excellent reference for practitioners. The first volume gives a thorough treatment of celestial mechanics and presents all the necessary mathematical details that a professional would need. The reader will appreciate the well-written chapters on numerical solution techniques for ordinary differential equations, as well as that on orbit determination. In the second volume applications to the rotation of earth and moon, to artificial earth satellites and to the planetary system are presented. The author addresses all aspects that are of importance in high-tech applications, such as the detailed gravitational fields of all planets and the earth, the oblateness of the earth, the radiation pressure and the atmospheric drag. The concluding part of this monumental treatise explains and details state-of-the-art professional and thoroughly-tested software for celestial mechanics.

Author : Victor Brumberg,Eugene V. Brumberg
Publisher : CRC Press
Page : 220 pages
File Size : 52,9 Mb
Release : 1999-07-22
Category : Science
ISBN : 9056992120

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Celestial Dynamics at High Eccentricities by Victor Brumberg,Eugene V. Brumberg Pdf

This book aims to extend the range of application of analytical and semi-analytical techniques of classical celestial mechanics for the case of motion in highly eccentric orbits. The technique, developed by the authors and described in detail here, is based on the traditional mean, true, or eccentric anomalies with the elliptic anomaly and corresponding Fourier expansions for Jacobi elliptic functions. It makes it possible to represent more effectively the motion of celestial objects in highly eccentric orbits, which until now has been studied mostly using numerical integration. The specific methodology described in the book is linked closely to mathematical software used widely in the West, and is therefore of relevance to researchers worldwide.

Author : Eugene Oks,Evgeniĭ Aleksandrovich Oks
Publisher : Unknown
Page : 0 pages
File Size : 45,5 Mb
Release : 2019
Category : Approximation theory
ISBN : 0750325127

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Analytical Advances in Quantum and Celestial Mechanics by Eugene Oks,Evgeniĭ Aleksandrovich Oks Pdf

This book is devoted primarily to recent advances in applying the approximate analytical method of the separation of rapid and slow subsystems to other quantum realms. Such systems include hydrogen atoms in a high-frequency laser field, rotator-dipoles in a high-frequency field, one-electron Rydberg quasimolecules in various fields, muonic-electronic helium atoms and the dynamical Stark broadening of spectral lines by plasma ions and electrons. The book also presents novel applications to some unrestricted three-body systems in celestial mechanics, such as a planet orbiting around a binary star or a star-planet-moon system. These results are practically important in the quest for achieving controlled nuclear fusion on Earth, as well as expanding practical applications of lasers and other related fields.

Author : NASA-University Conference on the Science and Technology of Space Exploration, Chicago, 1962
Publisher : Unknown
Page : 52 pages
File Size : 51,6 Mb
Release : 1963
Category : Astrodynamics
ISBN : STANFORD:36105024705233

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Celestial Mechanics and Space Flight Analysis by NASA-University Conference on the Science and Technology of Space Exploration, Chicago, 1962 Pdf

Author : Archie E. Roy
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400930537

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Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems by Archie E. Roy Pdf

The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d'Ampezzo, Italy between August 3 and August 13, 1987 under the title "Long Term Dynamical Behaviour of Natural and Artificial N-body Systems". The Institute was the latest in a series held in 1972, 1975, 1978, 1981, 1984 in dynamical astronomy, theoretical mechanics and celestial mechanics under the Directorship of Professor Victor Szebehely. These previous institutes, held in high esteem by the international community of research workers, have resulted in a series of well-received and valuable Proceedings. In correspondence with Professor Szebehely and in long discussions with him in Colorado in August 1985, I agreed to his request that I undertake the preparation of a new ASI. I was happy to do so knowing I could call upon his vast experience in overseeing such ASI's. The last quarter century has been a period in which increasingly rapid progress has been made in celestial mechanics and related subjects not only because of the appearance of new problems urgently requiring solution but also because of the advent of new analytical techniques and powerful computer hardware and software.

Author : Dirk Brouwer,Gerald M. Clemence
Publisher : Elsevier
Page : 611 pages
File Size : 53,6 Mb
Release : 2013-09-03
Category : Science
ISBN : 9781483225784

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Methods of Celestial Mechanics by Dirk Brouwer,Gerald M. Clemence Pdf

Methods of Celestial Mechanics provides a comprehensive background of celestial mechanics for practical applications. Celestial mechanics is the branch of astronomy that is devoted to the motions of celestial bodies. This book is composed of 17 chapters, and begins with the concept of elliptic motion and its expansion. The subsequent chapters are devoted to other aspects of celestial mechanics, including gravity, numerical integration of orbit, stellar aberration, lunar theory, and celestial coordinates. Considerable chapters explore the principles and application of various mathematical methods. This book is of value to mathematicians, physicists, astronomers, and celestial researchers.

Author : V. Rauschenbakh,M. Y. Ovchinnikov,Susan M.P. McKenna-Lawlor
Publisher : Springer Science & Business Media
Page : 397 pages
File Size : 51,7 Mb
Release : 2006-04-11
Category : Technology & Engineering
ISBN : 9780306480270

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Essential Spaceflight Dynamics and Magnetospherics by V. Rauschenbakh,M. Y. Ovchinnikov,Susan M.P. McKenna-Lawlor Pdf

Essential Spaceflight Dynamics and Magnetospherics describes, in the first instance, some of the key aspects of celestial mechanics and spaceflight dynamics. It begins with classical two and three body problems illustrative of the aesthetic aspects of applying analytical methods of investigation to celestial mechanics. Then, osculating orbital elements are introduced as well as analysis techniques sufficient to evaluate the influence of various disturbing forces on spacecraft. Next a theory of manoeuvres is outlined and the methodology of making interplanetary trajectory corrections. Ideas involving various approaches to orbital element determinations using measured data are also considered. The forces applied to a spacecraft can result in the development of torques that influence attitude motion and the effects of the most important of these are described in terms of equilibrium positions, periodic motions, steady-state and transient motions. Also considered is the problem of attitude control of a spacecraft using active and/or passive methods of orientation and stabilization. In addition, a more advanced treatment of the development of attitude control systems is provided.