Search Results for theory-of-orbits

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.

Author: Victory Szebehely

Publisher: Elsevier

ISBN: 9780323143462

Category: Science

Page: 684

View: 175

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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.
2012-12-02 By Victory Szebehely

Introduction - The Theory of Orbits from Epicycles to “ Chaos ” The subject of this book is the study of the orbits followed by a body ( mass point ) subjected to the gravitational attraction of a given number of other bodies ( mass ...

Author: Dino Boccaletti

Publisher: Springer Science & Business Media

ISBN: 3540589635

Category: Science

Page: 392

View: 622

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Half a century ago, S. Chandrasekhar wrote these words in the preface to his l celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ ... J Indeed, several of the problems of modern stellar dy namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con sidered from the point of view of celestial mechanics (the N-body problem with N » 1), fluid mechanics (the system is represented by a material con tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).
2003-10-08 By Dino Boccaletti

The purpose of this reference and handbook is to describe and to derive the analytic solutionsoftheequationsofsatellitemotionperturbedbyextraterrestrialandgeo- tential disturbances of the second order.

Author: Xu Guochang

Publisher: Springer

ISBN: 3642097286

Category: Science

Page: 230

View: 271

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The purpose of this reference and handbook is to describe and to derive the analytic solutionsoftheequationsofsatellitemotionperturbedbyextraterrestrialandgeo- tential disturbances of the second order. The equations of satellite motion perturbed by extraterrestrial disturbances are solved by means of discretization and appr- imated potential function as well as Gaussian equations. The equations perturbed by geopotential disturbances are solved by symbolic mathematical operations. The traditional problem of singularity in the solutions is solved by so-called singulari- free orbit theory. Simpli?ed disturbed equations of motion are proposed to simplify the solutions. Applications of the theory for analytic orbit determination are also discussed. Indeed, this is the ?rst book since the satellite era, which describes s- tematically the orbit theory with analytical solutions, with respect to all of extrat- restrial and geopotential disturbances of the second order, and the solutions are free of singularity. Based on such a theory, the algorithms of orbit determination can be renewed; deeper insight into the physics of disturbances becomes possible; the way to a variety of new applications and re?nements is opened. My primary knowledge of the orbit theory came from my education of mat- matics while studying physics and theoretical mechanics (1981). My ?rst practical experience with orbit came from the research activity at the Technical University (TU) Berlin on orbit corrections of the satellite altimetry data (1988–1992). The extensive experience on orbit came from the GPS/Galileo software development for orbit determination and geopotential mapping at the GFZ (2001–2004).
2010-10-19 By Xu Guochang

THEORY OF ORBIT DETERMINATION Determining orbits of natural and artificial celestial bodies is an essential step in the exploration and understanding of the Solar System. However, recent progress in the quality and quantity of data from ...

Author: Andrea Milani

Publisher: Cambridge University Press

ISBN: 9780521873895

Category: Mathematics

Page: 382

View: 104

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Presents new algorithms for determining orbits; ideal for graduate students and researchers in applied mathematics, physics, astronomy and aerospace engineering.
2010 By Andrea Milani

The first three chapters of this second volume are devoted to the theory of perturbations, starting from classical problems and arriving at the KAM theory, and to the introduction of the use of the Lie transform.

Author: Dino Boccaletti

Publisher: Springer

ISBN: 3662092417

Category:

Page: 440

View: 205

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Theory of Orbits treats celestial mechanics as well as stellar dynamics from the common point of view of orbit theory, making use of concepts and techniques from modern geometric mechanics. It starts with elementary Newtonian mechanics and ends with the dynamics of chaotic motion. The two volumes are meant for students in astronomy and physics alike. Prerequisite is a physicist's knowledge of calculus and differential geometry. The first three chapters of this second volume are devoted to the theory of perturbations, starting from classical problems and arriving at the KAM theory, and to the introduction of the use of the Lie transform. A whole chapter treats the theory of adiabatic invariants and its applications in celestial mechanics and stellar dynamics. Also the theory of resonances is illustrated and applications in both fields are shown. Classical and modern problems connected to periodic solutions are reviewed. The description of modern developments of the theory of chaos in conservative systems is the subject of a chapter in which an introduction is given to what happens in both near-integrable and non-integrable systems. The invaluable help provided by computers in the exploration of the long-time behaviour of dynamical systems is acknowledged in a final chapter, where some numerical algorithms and their applications both to systems with few degrees of freedom and to large "N"-body systems are illustrated.
2014-01-15 By Dino Boccaletti

Author: Simon Juden

Publisher:

ISBN: OCLC:59642608

Category:

Page:

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1995 By Simon Juden

In tracing the history of the accepted theory of orbits it will be found , that in the earlier efforts observation was more conspicuously relied upon than demonstration . Originally the elliptical theory of orbits is simply the result ...

Author: H. G. Rush

Publisher:

ISBN: UOM:39015049796686

Category: Orbits

Page: 135

View: 189

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1887 By H. G. Rush

The first three chapters of this second volume are devoted to the theory of perturbations, starting from classical problems and arriving at the KAM theory, and to the introduction of the use of the Lie transform.

Author: Dino Boccaletti

Publisher: Springer

ISBN: 3540603557

Category: Science

Page: 423

View: 572

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Half a century ago, S. Chandrasekhar wrote these words in the preface to his 1 celebrated and successful book: In this monograph an attempt has been made to present the theory of stellar dy namics as a branch of classical dynamics - a discipline in the same general category as celestial mechanics. [ ... ] Indeed, several of the problems of modern stellar dy namical theory are so severely classical that it is difficult to believe that they are not already discussed, for example, in Jacobi's Vorlesungen. Since then, stellar dynamics has developed in several directions and at var ious levels, basically three viewpoints remaining from which to look at the problems encountered in the interpretation of the phenomenology. Roughly speaking, we can say that a stellar system (cluster, galaxy, etc.) can be con sidered from the point of view of celestial mechanics (the N-body problem with N» 1), fluid mechanics (the system is represented by a material con tinuum), or statistical mechanics (one defines a distribution function for the positions and the states of motion of the components of the system).
2002-08-21 By Dino Boccaletti

This book focuses on the theory and design of special space orbits.

Author: Yasheng Zhang

Publisher: Springer

ISBN: 9811029474

Category: Technology & Engineering

Page: 243

View: 412

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This book focuses on the theory and design of special space orbits. Offering a systematic and detailed introduction to the hovering orbit, spiral cruising orbit, multi-target rendezvous orbit, initiative approaching orbit, responsive orbit and earth pole-sitter orbit, it also discusses the concept, theory, design methods and application of special space orbits, particularly the design and control method based on kinematics and astrodynamics. In addition the book presents the latest research and its application in space missions. It is intended for researchers, engineers and postgraduates, especially those working in the fields of orbit design and control, as well as space-mission planning and research.
2016-12-12 By Yasheng Zhang

With the successful launch of the first artificial earth satellite in the 1950s, design theories and methods of spacecraft orbit have been developing rapidly. The primary missions of a spacecraft at that time were to conduct ...

Author: Yasheng Zhang

Publisher: Springer

ISBN: 9789811029486

Category: Technology & Engineering

Page: 243

View: 844

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This book focuses on the theory and design of special space orbits. Offering a systematic and detailed introduction to the hovering orbit, spiral cruising orbit, multi-target rendezvous orbit, initiative approaching orbit, responsive orbit and earth pole-sitter orbit, it also discusses the concept, theory, design methods and application of special space orbits, particularly the design and control method based on kinematics and astrodynamics. In addition the book presents the latest research and its application in space missions. It is intended for researchers, engineers and postgraduates, especially those working in the fields of orbit design and control, as well as space-mission planning and research.
2016-11-25 By Yasheng Zhang

Here we discuss the concept of bi-circular orbits and bi-circular orbit perturbations. It is shown how an elliptical orbit can be decomposed into two counter-rotating circular orbits. In this way, orbital dynamics can be approximated ...

Author: Drazen Svehla

Publisher: Springer

ISBN: 9783319768731

Category: Science

Page: 537

View: 424

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This book on space geodesy presents pioneering geometrical approaches in the modelling of satellite orbits and gravity field of the Earth, based on the gravity field missions CHAMP, GRACE and GOCE in the LEO orbit. Geometrical approach is also extended to precise positioning in space using multi-GNSS constellations and space geodesy techniques in the realization of the terrestrial and celestial reference frame of the Earth. This book addresses major new developments that were taking place in space geodesy in the last decade, namely the availability of GPS receivers onboard LEO satellites, the multitude of the new GNSS satellite navigation systems, the huge improvement in the accuracy of satellite clocks and the revolution in the determination of the Earth's gravity field with dedicated satellite missions.
2018-07-02 By Drazen Svehla

It owes its existence to certain problems from number theory, algebra, and geometry, which appeared in the works of ... is given by the orbits of a group G acting on a set X . On the other hand, invariant theory noticeably influenced ...

Author: V. L. Popov

Publisher: American Mathematical Soc.

ISBN: 9780821853351

Category: Invariants

Page: 245

View: 429

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The history of invariant theory spans nearly a century and a half, with roots in certain problems from number theory, algebra, and geometry appearing in the work of Gauss, Jacobi, Eisenstein, and Hermite. Although the connection between invariants and orbits was essentially discovered in the work of Aronhold and Boole, a clear understanding of this connection had not been achieved until recently, when invariant theory was in fact subsumed by a general theory of algebraic groups. Written by one of the major leaders in the field, this book provides an excellent, comprehensive exposition of invariant theory. Its point of view is unique in that it combines both modern and classical approaches to the subject. The introductory chapter sets the historical stage for the subject, helping to make the book accessible to nonspecialists.
2011-01-05 By V. L. Popov

The idea for this book emerged when we realized that documentation on the methods, models and tools of orbit determination was either spread over numerous technical and scientific publications, or hidden in software descriptions that are ...

Author: Oliver Montenbruck

Publisher: Springer Science & Business Media

ISBN: 354067280X

Category: Nature

Page: 369

View: 436

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Satellite Orbits -Models, Methods, and Applications has been written as a compre hensive textbook that guides the reader through the theory and practice of satellite orbit prediction and determination. Starting from the basic principles of orbital mechanics, it covers elaborate force models as weH as precise methods of satellite tracking and their mathematical treatment. A multitude of numerical algorithms used in present-day satellite trajectory computation is described in detail, with proper focus on numerical integration and parameter estimation. The wide range of levels provided renders the book suitable for an advanced undergraduate or gradu ate course on spaceflight mechanics, up to a professional reference in navigation, geodesy and space science. Furthermore, we hope that it is considered useful by the increasing number of satellite engineers and operators trying to obtain a deeper understanding of flight dynamics. The idea for this book emerged when we realized that documentation on the methods, models and tools of orbit determination was either spread over numerous technical and scientific publications, or hidden in software descriptions that are not, in general, accessible to a wider community. Having worked for many years in the field of spaceflight dynamics and satellite operations, we tried to keep in c10se touch with questions and problems that arise during daily work, and to stress the practical aspects of orbit determination. Nevertheless, our interest in the underlying physics motivated us to present topics from first principles, and make the book much more than just a cookbook on spacecraft trajectory computation.

For the orbit of Mars . Dr. G. M. Clemence [ 7 ] is completing a new theory by Hansen's method that promises to be a great improvement on the present theory . For the outer planets . Uranus . Neptune and Pluto , new general theories are ...

Author: Garrett Birkhoff

Publisher: American Mathematical Soc.

ISBN: 0821873474

Category:

Page: 195

View: 281

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1959-12-31 By Garrett Birkhoff

Author: George Contopoulos

Publisher:

ISBN: LCCN:66008119

Category: Orbits

Page: 380

View: 224

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Author: Peter Musen

Publisher:

ISBN: UIUC:30112106635813

Category: Lunar theory

Page: 26

View: 599

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1965 By Peter Musen

65 PENETRATING AND NON-PENETRATING ORBITS The BohrStoner scheme of electron configuration in atoms has shown that the alkali atoms consist of a ... The spectra observed in alkali metals were first treated on the basis of Bohr theory.

Author: K.P. Rajappan Nair

Publisher: MJP Publisher

ISBN:

Category: Science

Page: 604

View: 394

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Spectroscopy is an indispensable tool in understanding physical and chemical structure, and today verysophisticated spectroscopic instruments are available with modern data processing techniques. This bookcovers the elementary and basic aspects of atomic spectroscopy like Bohr’s theory and atomic physics up to thelatest developments including laser cooling, Bose–Einstein condensates and atom lasers. Spectroscopy playsa major role in every field of science and this book would be valuable for physicists, chemists and biologists.
2019-06-06 By K.P. Rajappan Nair

Consider a complex semisimple Lie group G with Lie algebra g and Weyl group W. In this book, we present a geometric perspective on the following circle of ideas: polynomials The "vertices" of this graph are some of the most important ...

Author: Walter Borho

Publisher: Springer Science & Business Media

ISBN: 0817634738

Category: Mathematics

Page: 134

View: 827

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1. The Subject Matter. Consider a complex semisimple Lie group G with Lie algebra g and Weyl group W. In this book, we present a geometric perspective on the following circle of ideas: polynomials The "vertices" of this graph are some of the most important objects in representation theory. Each has a theory in its own right, and each has had its own independent historical development. - A nilpotent orbit is an orbit of the adjoint action of G on g which contains the zero element of g in its closure. (For the special linear group 2 G = SL(n,C), whose Lie algebra 9 is all n x n matrices with trace zero, an adjoint orbit consists of all matrices with a given Jordan canonical form; such an orbit is nilpotent if the Jordan form has only zeros on the diagonal. In this case, the nilpotent orbits are classified by partitions of n, given by the sizes of the Jordan blocks.) The closures of the nilpotent orbits are singular in general, and understanding their singularities is an important problem. - The classification of irreducible Weyl group representations is quite old.
1989-12-01 By Walter Borho

Author: William A. Mersman

Publisher:

ISBN: NASA:31769000421456

Category: Artificial satellites

Page: 34

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Author:

Publisher:

ISBN: OCLC:164996663

Category:

Page:

View: 914

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1957 By