Recent Advances in Dynamical Astronomy
Recent Advances in Dynamical Astronomy

Author: B.D. Tapley

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 476

ISBN-13: 9401026114

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IX LIST OF PRINCIPAL SPEAKERS XI LIST OF PARTICIPANTS 1. REGULARIZATION E. STIEFEL / A Linear Theory of the Perturbed Two-Body Problem (Regul- ization) 3 J. WALDVOGEL / Collision Singularities in Gravitational Problems 21 D. C. HEGGIE / Regularization Using a Time-Transformation Only 34 J. BAUMGAR TE / Stabilization of the Differential Equations of Keplerian Motion 38 F. NAHON / The Particular Solutions of Levi-Civita 45 O. GODAR T / Example ofIntegration of Strongly Oscillating Systems 53 w. BLACK / The Application of Recurrence Relations to Special Perturbation Methods 61 D. G. BETTIS / Numerical Solution of Ordinary Differential Equations (Abstract) 71 II. THE THREE-BODY PROBLEM V. SZEBEHELY / Recent Advances in the Problem of Three Bodies 75 R. F. ARENSTORF / Periodic Elliptic Motion in the Problem of Three Bodies (Abstract) 107 G. KATSIARIS and c. L. GOUDAS / On a Conjecture by Poincare 109 G. KATSIARIS / The Three-Dimensional Elliptic Problem 118 P. G. KAZANTZIS / Second and Third Order Variations of the Three Dimensional Restricted Problem 135 c. G. ZAGOURAS / Planar Periodic Orbits Using Second and Third Variations 146 E. RABE / Elliptic Restricted Problem: Fourth-Order Stability Analysis of the Triangular Points 156 P. GUILLAUME / A Linear Description of the Second Species Solutions 161 III. THE N-BODY PROBLEM AND STELLAR DYNAMICS G. CONTOPOULOS / Problems of Stellar Dynamics 177 w. T. KYNER / Invariant Manifolds in Celestial Mechanics 192 s. J.

Order and Chaos in Dynamical Astronomy
Order and Chaos in Dynamical Astronomy

Author: George Contopoulos

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 633

ISBN-13: 3662049171

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This book is one of the first to provide a general overview of order and chaos in dynamical astronomy. The progress of the theory of chaos has a profound impact on galactic dynamics. It has even invaded celestial mechanics, since chaos was found in the solar system which in the past was considered as a prototype of order. The book provides a unifying approach to these topics from an author who has spent more than 50 years of research in the field. The first part treats order and chaos in general. The other two parts deal with order and chaos in galaxies and with other applications in dynamical astronomy, ranging from celestial mechanics to general relativity and cosmology.

Jacobi Dynamics
Jacobi Dynamics

Author: V.I. Ferronsky

Publisher: Springer Science & Business Media

Published: 1986-12-31

Total Pages: 394

ISBN-13: 9789027724182

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This book sets forth and builds upon the fundamentals of the dynamics of natural systems in formulating the problem presented by Jacobi in his famous lecture series "Vorlesungen tiber Dynamik" (Jacobi, 1884). In the dynamics of systems described by models of discrete and continuous media, the many-body problem is usually solved in some approximation, or the behaviour of the medium is studied at each point of the space it occupies. Such an approach requires the system of equations of motion to be written in terms of space co-ordinates and velocities, in which case the requirements of an internal observer for a detailed description of the processes are satisfied. In the dynamics discussed here we study the time behaviour of the fundamental integral characteristics of the physical system, i. e. the Jacobi function (moment of inertia) and energy (potential, kinetic and total), which are functions of mass density distribution, and the structure of a system. This approach satisfies the requirements of an external observer. It is designed to solve the problem of global dynamics and the evolution of natural systems in which the motion of the system's individual elements written in space co-ordinates and velocities is of no interest. It is important to note that an integral approach is made to internal and external interactions of a system which results in radiation and absorption of energy. This effect constitutes the basic physical content of global dynamics and the evolution of natural systems.

Dynamics of Close Binary Systems
Dynamics of Close Binary Systems

Author: Zdenek Kopal

Publisher: Springer Science & Business Media

Published: 1978-08-31

Total Pages: 536

ISBN-13: 9789027708205

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The aim of the present book will be to provide a comprehensive account of our present knowledge of the theory of dynamical phenomena exhibited by elose binary systems; and on the basis of such phenomena as have been attested by available observations to outline probable evolutionary trends of such systems in the course of time. The evolution of the stars - motivated by nuelear as weIl as gravitation al energy sources - constitutes nowadays a well-established branch of stellar astronomy. No theo ries of such an evolution are as yet sufficently specific - let alone infallible - not to require continual tests by a confrontation of their consequences with the observed prop erties of actual stars at different stages of their evolution. The discriminating power of such tests depends, of course, on the range of information offered by the test objects. Single stars which move alone in space are now known to represent only a minority of objects constituting our Galaxy (cf. Chapter 1-2); and are, moreover, not very revealing of their basic physical characteristics - such as their masses or absolute dimensions. If there were no binary systems in the sky, the only star whose vital statistics would be fully known to us would be our Sun.

Reference Coordinate Systems for Earth Dynamics
Reference Coordinate Systems for Earth Dynamics

Author: E.M. Gaposchkin

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 393

ISBN-13: 9400984561

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Proceedings of the 56th Colloquium of the International Astronomical Union held in Warsaw, Poland, September 8-12, 1980

Kinematics, Dynamics and Structure of the Milky Way
Kinematics, Dynamics and Structure of the Milky Way

Author: W.L.H. Shuter

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 384

ISBN-13: 9400970609

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The idea of holding this workshop on "The Jllilky Way" arose at the conference dinner of a meeting on "Regions of Recent Star Formation" held at Penticton in June 1981. Leo Blitz (now at the University of Maryland) and I decided that there was a need, and agreed that we would organize one in Vancouver in the Spring of 1982. The purpose of the workshop was to have an intensive exchange of ideas between some of the most active workers in the field regarding the recent work which has been significantly changing our concepts of the Milky Way. To achieve this we limited the number of participants, and planned the program so that there was ample time for discussion. The meeting appeared to work very well, both scientifically and socially, and this volume contains 50 of the 55 papers that were The discussion was very lengthy, but since the papers were presented. written up after the meeting many of the points raised have been in the publications, and it seems pointless to reproduce it incorporated here. Leo and I would like to thank the many people who helped to make the meeting a success: at UBC) and Frank J. Kerr (Provost of MPSE C.V. Finnegan (Dean of Science at the University of Maryland) who welcomed the participants on behalf of the sponsoring Universities. Bart Bok who opened the scientific proceedings, and Maarten Schmidt who gave the closing summary.

Periodic Orbits: F. R. Moulton’s Quest for a New Lunar Theory
Periodic Orbits: F. R. Moulton’s Quest for a New Lunar Theory

Author: Craig A. Stephenson

Publisher: American Mathematical Soc.

Published: 2021-05-19

Total Pages: 255

ISBN-13: 1470456710

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Owing to its simple formulation and intractable nature, along with its application to the lunar theory, the three-body problem has since it was first studied by Newton in the Principia attracted the attention of many of the world's most gifted mathematicians and astronomers. Two of these, Euler and Lagrange, discovered the problem's first periodic solutions. However, it was not until Hill's discovery in the late 1870s of the variational orbit that the importance of the periodic solutions was fully recognized, most notably by Poincaré, but also by others such as Sir George Darwin. The book begins with a detailed description of the early history of the three-body problem and its periodic solutions, with chapters dedicated to the pioneering work of Hill, Poincaré, and Darwin. This is followed by the first in-depth account of the contribution to the subject by the mathematical astronomer Forest Ray Moulton and his research students at the University of Chicago. The author reveals how Moulton's Periodic Orbits, published in 1920 and running to some 500 pages, arose from Moulton's ambitious goal of creating an entirely new lunar theory. The methods Moulton developed in the pursuit of this goal are described and an examination is made of both the reception of his work and his legacy for future generations of researchers.

X-Ray Astronomy
X-Ray Astronomy

Author: R. Giacconi

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 456

ISBN-13: 9401021058

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It was about fourteen years ago that some of us became intrigued with the idea of searching the sky for X-ray and gamma-ray sources other than the Sun, the only celestial emitter of high-energy photons known at that time. It was, of course, clear that an effort in this direction would not have been successful unless there occurred, somewhere in space, processes capable of producing high-energy photons much more efficiently than the processes responsible for the radiative emission of the Sun or of ordinary stars. The possible existence of such processes became the subject of much study and discussion. As an important part of this activity, I wish to recall a one-day conference on X-ray astronomy held at the Smithsonian Astrophysical Observatory in 1960. The theoretical predictions did not provide much encouragement. While several 'unusual' celestial objects were pin-pointed as possible, or even likely, sources of X-rays, it did not look as if any of them would be strong enough to be observable with instru mentation not too far beyond the state of the art. Fortunately, we did not allow our selves to be dissuaded. As far as I am personally concerned, I must admit that my main motivation for pressing forward was a deep-seated faith in the boundless re sourcefulness of nature, which so often leaves the most daring imagination of man far behind.

Introduction to Astronomical Photometry
Introduction to Astronomical Photometry

Author: M. Golay

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 376

ISBN-13: 9401021694

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The material given in this 'Introduction to astronomical photometry' is the subject matter of a lecture at the University of Geneva. It is, therefore, intended for those students, physicists or mathematicians, who have completed their bachelor's degree or diploma, and are intending to work for their Ph.D. in astronomy. We assume then the elementary ideas of astrophysics, magnitude, colour index, spectral classes, luminosity classes, gradient, atmospheric extinction are already known. The student may find it useful to re-read the work of Schatzman [1], Dufay [2] and Aller [254] before embarking upon the study of this 'Introduction to astronomical photometry'. It is not our aim in this book to deal with every aspect of stellar photometry. On the contrary, we shall restriet ourselves to looking at subjects ofwhich knowledge seems to us essential for someone who has to use photometrie quantities in his astronomical research. We are, therefore, keeping the interests of the photometrie measurements user partieularly in mind. We shall only discuss very superficially the technical prob lems and reduction methods for atmospheric extinction. These problems are dealt with very clearly in Astronomical Techniques [3]; the first by A. Lallemand, H. L.

Infrared and Submillimeter Astronomy
Infrared and Submillimeter Astronomy

Author: G.G. Fazio

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 225

ISBN-13: 9401012113

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The Symposium on Infrared and Submillimeter Astronomy was held in Philadelphia, Pennsylvania, U.S.A., on June 8-10, 1976, as an activity associated with the Nineteenth Plenary Meeting of the Committee on Space Research (CaSPAR). The Symposium was sponsored jointly by CaSPAR, the International Astronomical Union (IAU) and the International Union of Radio Science CURSI). caSPAR is an interdisciplinary scientific organization, established by the International Council of Scientific Unions in 1958, to, in the words of its charter, "provide the world scientific community with the means whereby it may exploit the possibilities of satellites and space probes of all kinds for scientific purposes and exchange the resulting data on a co operative basis." The purpose of this particular CaSPAR Sympo sium was to present new results in infrared and submillimeter astronomy obtained by observations on aircraft, high altitude balloons, rockets, satellites, and space probes. Topics dis cussed included the Sun, the solar system, galactic and extra galactic objects as well as the cosmic background radiation. Instrumentation for observations in infrared and submillimeter astronomy was also discussed, with particular emphasis on future programs from space observatories.