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Author : Aurel Wintner
Publisher : Unknown
Page : 472 pages
File Size : 41,7 Mb
Release : 1941
Category : Science
ISBN : UOM:39015002003864
Author : Aurel Frederick Wintner
Publisher : Unknown
Page : 0 pages
File Size : 43,9 Mb
Release : 1941
Category : Celestial mechanics
ISBN : LCCN:nun00509730
Author : Aurel Wintner
Publisher : Courier Corporation
Page : 468 pages
File Size : 52,8 Mb
Release : 2014-06-18
Category : Science
ISBN : 9780486780603
With this 1941 monograph, Aurel Wintner joined Poincaré, Birkhoff, and others in placing celestial mechanics on a sound mathematical basis. The product of many years of work by the author, it remains an extremely valuable contribution to the literature of this field. Starting with a review of dynamical operations, the treatment advances to local and non-local questions, dynamical systems, the problem of two bodies and the problem of several bodies, and an introduction to the restricted problem. Suitable for advanced undergraduates and graduate students of physics, the text is amply supplemented by a substantial section of notes and references in which a great deal of the historical literature from which it derives is discussed.
Author : Victor A. Brumberg
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642794544
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 : Dora Musielak
Publisher : Springer Nature
Page : 228 pages
File Size : 52,9 Mb
Release : 2022-11-01
Category : Science
ISBN : 9783031123221
The intention of this book is to shine a bright light on the intellectual context of Euler’s contributions to physics and mathematical astronomy. Leonhard Euler is one of the most important figures in the history of science, a blind genius who introduced mathematical concepts and many analytical tools to help us understand and describe the universe. Euler also made a monumental contribution to astronomy and orbital mechanics, developing what he called astronomia mechanica. Orbital mechanics of artificial satellites and spacecraft is based on Euler’s analysis of astromechanics. However, previous books have often neglected many of his discoveries in this field. For example, orbital mechanics texts refer to the five equilibrium points in the Sun-Earth-Moon system as Lagrange points, failing to credit Euler who first derived the differential equations for the general n-body problem and who discovered the three collinear points in the three-body problem of celestial mechanics. These equilibrium points are essential today in space exploration; the James Webb Space Telescope (successor to the Hubble), for example, now orbits the Sun near L2, one of the collinear points of the Sun-Earth-Moon system, while future missions to study the universe will place observatories in orbit around Sun-Earth and Earth-Moon equilibrium points that should be properly called Euler-Lagrange points. In this book, the author uses Euler’s memoirs, correspondence, and other scholarly sources to explore how he established the mathematical groundwork for the rigorous study of motion in our Solar System. The reader will learn how he studied comets and eclipses, derived planetary orbits, and pioneered the study of planetary perturbations, and how, old and blind, Euler put forward the most advanced lunar theory of his time.
Author : Elena Bannikova,Massimo Capaccioli
Publisher : Springer
Page : 0 pages
File Size : 49,7 Mb
Release : 2022-09-13
Category : Science
ISBN : 3031045750
This book provides an introduction to classical celestial mechanics. It is based on lectures delivered by the authors over many years at both Padua University (MC) and V.N. Karazin Kharkiv National University (EB). The book aims to provide a mathematical description of the gravitational interaction of celestial bodies. The approach to the problem is purely formal. It allows the authors to write equations of motion and solve them to the greatest degree possible, either exactly or by approximate techniques, when there is no other way. The results obtained provide predictions that can be compared with the observations. Five chapters are supplemented by appendices that review certain mathematical tools, deepen some questions (so as not to interrupt the logic of the mainframe with heavy technicalities), give some examples, and provide an overview of special functions useful here, as well as in many other fields of physics. The authors also present the original investigation of torus potential. This book is aimed at senior undergraduate students of physics or astrophysics, as well as graduate students undertaking a master’s degree or Ph.D.
Author : Gleb Aleksandrovich Chebotarev
Publisher : Unknown
Page : 360 pages
File Size : 47,8 Mb
Release : 1967
Category : Celestial mechanics
ISBN : UCAL:B4179120
Author : George William Collins
Publisher : Unknown
Page : 166 pages
File Size : 54,7 Mb
Release : 1989
Category : Celestial mechanics
ISBN : UCAL:B4399149
Author : Victor G. Szebehely,Hans Mark
Publisher : John Wiley & Sons
Page : 320 pages
File Size : 48,9 Mb
Release : 2008-07-11
Category : Technology & Engineering
ISBN : 9783527617791
A fascinating introduction to the basic principles of orbital mechanics It has been three hundred years since Isaac Newton first formulated laws to explain the orbits of the Moon and the planets of our solar system. In so doing he laid the groundwork for modern science's understanding of the workings of the cosmos and helped pave the way to the age of space exploration. Adventures in Celestial Mechanics offers students an enjoyable way to become acquainted with the basic principles involved in the motions of natural and human-made bodies in space. Packed with examples in which these principles are applied to everything from a falling stone to the Sun, from space probes to galaxies, this updated and revised Second Edition is an ideal introduction to celestial mechanics for students of astronomy, physics, and aerospace engineering. Other features that helped make the first edition of this book the text of choice in colleges and universities across North America include: * Lively historical accounts of important discoveries in celestial mechanics and the men and women who made them * Superb illustrations, photographs, charts, and tables * Helpful chapter-end examples and problem sets
Author : Ralph Abraham
Publisher : CRC Press
Page : 850 pages
File Size : 44,7 Mb
Release : 2019-04-24
Category : Science
ISBN : 9780429709050
Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.
Author : Victor Brumberg
Publisher : Springer
Page : 236 pages
File Size : 50,8 Mb
Release : 2011-12-22
Category : Science
ISBN : 3642794556
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 : Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Neishtadt
Publisher : Springer Science & Business Media
Page : 505 pages
File Size : 51,5 Mb
Release : 2007-07-05
Category : Mathematics
ISBN : 9783540489269
The main purpose of the book is to acquaint mathematicians, physicists and engineers with classical mechanics as a whole, in both its traditional and its contemporary aspects. As such, it describes the fundamental principles, problems, and methods of classical mechanics, with the emphasis firmly laid on the working apparatus, rather than the physical foundations or applications. Chapters cover the n-body problem, symmetry groups of mechanical systems and the corresponding conservation laws, the problem of the integrability of the equations of motion, the theory of oscillations and perturbation theory.
Author : Donald Saari,Zhihong Xia
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 49,7 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821805664
This book contains selected papers from the AMS-IMS-SIAM Joint Summer Research Conference on Hamiltonian Systems and Celestial Mechanics held in Seattle in June 1995. The symbiotic relationship of these two topics creates a natural combination for a conference on dynamics. The topics covered include twist maps, the Aubrey-Mather theory, Arnold diffusion, qualitative and topological studies of systems, and variational methods, as well as specific topics such as Melnikov's procedure and the singularity properties of particular systems. As one of the few books that addresses both Hamiltonian systems and celestial mechanics, this volume offers emphasis on new issues and unsolved problems. Many of the papers give new results, yet the editors purposely included some exploratory papers based on numerical computations, a section on unsolved problems, and papers that pose conjectures while developing what is known. It features open research problems, and papers on central configurations.
Author : Pini Gurfil,P. Kenneth Seidelmann
Publisher : Springer
Page : 522 pages
File Size : 47,6 Mb
Release : 2016-07-28
Category : Science
ISBN : 9783662503706
This volume is designed as an introductory text and reference book for graduate students, researchers and practitioners in the fields of astronomy, astrodynamics, satellite systems, space sciences and astrophysics. The purpose of the book is to emphasize the similarities between celestial mechanics and astrodynamics, and to present recent advances in these two fields so that the reader can understand the inter-relations and mutual influences. The juxtaposition of celestial mechanics and astrodynamics is a unique approach that is expected to be a refreshing attempt to discuss both the mechanics of space flight and the dynamics of celestial objects. “Celestial Mechanics and Astrodynamics: Theory and Practice” also presents the main challenges and future prospects for the two fields in an elaborate, comprehensive and rigorous manner. The book presents homogenous and fluent discussions of the key problems, rendering a portrayal of recent advances in the field together with some basic concepts and essential infrastructure in orbital mechanics. The text contains introductory material followed by a gradual development of ideas interweaved to yield a coherent presentation of advanced topics.
Author : Hansjörg Geiges
Publisher : Cambridge University Press
Page : 241 pages
File Size : 44,7 Mb
Release : 2016-03-24
Category : Mathematics
ISBN : 9781107125407
A first course in celestial mechanics emphasising the variety of geometric ideas that have shaped the subject.