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The Geometry Of Celestial Mechanics
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Book Synopsis The Geometry of Celestial Mechanics by : Hansjörg Geiges
Download or read book The Geometry of Celestial Mechanics written by Hansjörg Geiges and published by Cambridge University Press. This book was released on 2016-03-24 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: A first course in celestial mechanics emphasising the variety of geometric ideas that have shaped the subject.
Book Synopsis Lectures on the Geometry of Numbers by : Carl Ludwig Siegel
Download or read book Lectures on the Geometry of Numbers written by Carl Ludwig Siegel and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Carl Ludwig Siegel gave a course of lectures on the Geometry of Numbers at New York University during the academic year 1945-46, when there were hardly any books on the subject other than Minkowski's original one. This volume stems from Siegel's requirements of accuracy in detail, both in the text and in the illustrations, but involving no changes in the structure and style of the lectures as originally delivered. This book is an enticing introduction to Minkowski's great work. It also reveals the workings of a remarkable mind, such as Siegel's with its precision and power and aesthetic charm. It is of interest to the aspiring as well as the established mathematician, with its unique blend of arithmetic, algebra, geometry, and analysis, and its easy readability.
Book Synopsis Relativistic Celestial Mechanics of the Solar System by : Sergei Kopeikin
Download or read book Relativistic Celestial Mechanics of the Solar System written by Sergei Kopeikin and published by John Wiley & Sons. This book was released on 2011-10-25 with total page 897 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative book presents the theoretical development of gravitational physics as it applies to the dynamics of celestial bodies and the analysis of precise astronomical observations. In so doing, it fills the need for a textbook that teaches modern dynamical astronomy with a strong emphasis on the relativistic aspects of the subject produced by the curved geometry of four-dimensional spacetime. The first three chapters review the fundamental principles of celestial mechanics and of special and general relativity. This background material forms the basis for understanding relativistic reference frames, the celestial mechanics of N-body systems, and high-precision astrometry, navigation, and geodesy, which are then treated in the following five chapters. The final chapter provides an overview of the new field of applied relativity, based on recent recommendations from the International Astronomical Union. The book is suitable for teaching advanced undergraduate honors programs and graduate courses, while equally serving as a reference for professional research scientists working in relativity and dynamical astronomy. The authors bring their extensive theoretical and practical experience to the subject. Sergei Kopeikin is a professor at the University of Missouri, while Michael Efroimsky and George Kaplan work at the United States Naval Observatory, one of the world?s premier institutions for expertise in astrometry, celestial mechanics, and timekeeping.
Book Synopsis Stability and Chaos in Celestial Mechanics by : Alessandra Celletti
Download or read book Stability and Chaos in Celestial Mechanics written by Alessandra Celletti and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This overview of classical celestial mechanics focuses the interplay with dynamical systems. Paradigmatic models introduce key concepts – order, chaos, invariant curves and cantori – followed by the investigation of dynamical systems with numerical methods.
Book Synopsis Lectures on Celestial Mechanics by : Carl L. Siegel
Download or read book Lectures on Celestial Mechanics written by Carl L. Siegel and published by Springer Science & Business Media. This book was released on 1995-02-15 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book represents to a large extent the translation of the German "Vorlesungen über Himmelsmechanik" by C. L. Siegel. The demand for a new edition and for an English translation gave rise to the present volume which, however, goes beyond a mere translation. To take account of recent work in this field a number of sections have been added, especially in the third chapter which deals with the stability theory. Still, it has not been attempted to give a complete presentation of the subject, and the basic prganization of Siegel's original book has not been altered. The emphasis lies in the development of results and analytic methods which are based on the ideas of H. Poincare, G. D. Birkhoff, A. Liapunov and, as far as Chapter I is concerned, on the work of K. F. Sundman and C. L. Siegel. In recent years the measure-theoretical aspects of mechanics have been revitalized and have led to new results which will not be discussed here. In this connection we refer, in particular, to the interesting book by V. I. Arnold and A. Avez on "Problemes Ergodiques de la Mecanique Classique", which stresses the interaction of ergodic theory and mechanics. We list the points in which the present book differs from the German text. In the first chapter two sections on the tri pie collision in the three body problem have been added by C. L. Siegel.
Book Synopsis Celestial Mechanics by : Alessandra Celletti
Download or read book Celestial Mechanics written by Alessandra Celletti and published by Springer Science & Business Media. This book was released on 2007-06-24 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to demonstrate to a wider audience, as well as to a more skilled audience, the many fascinating aspects of modern celestial mechanics. It sets out to do this without the use of mathematics. After giving the reader the technical tools needed for a basic understanding of the underlying physical phenomena (using only elementary mathematics), facts and figures are provided on historical events, modern discoveries and future applications. Contents are divided into major topics where the three "souls" of modern celestial mechanics (dynamical systems, Solar System and stellar systems, spaceflight dynamics) play a major role.
Book Synopsis Second Year Calculus by : David M. Bressoud
Download or read book Second Year Calculus written by David M. Bressoud and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.
Book Synopsis Mathematical Aspects of Classical and Celestial Mechanics by : Vladimir I. Arnold
Download or read book Mathematical Aspects of Classical and Celestial Mechanics written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2007-07-05 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Orbital Mechanics for Engineering Students by : Howard D. Curtis
Download or read book Orbital Mechanics for Engineering Students written by Howard D. Curtis and published by Elsevier. This book was released on 2009-10-26 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: Orbital Mechanics for Engineering Students, Second Edition, provides an introduction to the basic concepts of space mechanics. These include vector kinematics in three dimensions; Newton's laws of motion and gravitation; relative motion; the vector-based solution of the classical two-body problem; derivation of Kepler's equations; orbits in three dimensions; preliminary orbit determination; and orbital maneuvers. The book also covers relative motion and the two-impulse rendezvous problem; interplanetary mission design using patched conics; rigid-body dynamics used to characterize the attitude of a space vehicle; satellite attitude dynamics; and the characteristics and design of multi-stage launch vehicles. Each chapter begins with an outline of key concepts and concludes with problems that are based on the material covered. This text is written for undergraduates who are studying orbital mechanics for the first time and have completed courses in physics, dynamics, and mathematics, including differential equations and applied linear algebra. Graduate students, researchers, and experienced practitioners will also find useful review materials in the book. - NEW: Reorganized and improved discusions of coordinate systems, new discussion on perturbations and quarternions - NEW: Increased coverage of attitude dynamics, including new Matlab algorithms and examples in chapter 10 - New examples and homework problems
Book Synopsis Geometry of Continued Fractions by : Oleg Karpenkov
Download or read book Geometry of Continued Fractions written by Oleg Karpenkov and published by Springer Science & Business Media. This book was released on 2013-08-15 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.
Book Synopsis Rational Mechanics by : R. Catesby Taliaferro
Download or read book Rational Mechanics written by R. Catesby Taliaferro and published by Courier Corporation. This book was released on 2014-09-17 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from a classic Notre Dame undergraduate course on the study of the motion of bodies, this volume stresses the history of science as well as the relevant physics and mathematics. Starting with ancient Greek celestial mechanics, topics include the Keplerian Revolution, displacement and kinematics, the special theory of relativity, and much more. 2013 edition.
Book Synopsis Celestial Mechanics and Astrodynamics: Theory and Practice by : Pini Gurfil
Download or read book Celestial Mechanics and Astrodynamics: Theory and Practice written by Pini Gurfil and published by Springer. This book was released on 2016-07-28 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Geometry of Celestial Mechanics by : Hansjörg Geiges
Download or read book The Geometry of Celestial Mechanics written by Hansjörg Geiges and published by Cambridge University Press. This book was released on 2016-03-24 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.
Book Synopsis Symplectic Geometric Algorithms for Hamiltonian Systems by : Kang Feng
Download or read book Symplectic Geometric Algorithms for Hamiltonian Systems written by Kang Feng and published by Springer Science & Business Media. This book was released on 2010-10-18 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Symplectic Geometric Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development of numerical methodology for Hamiltonian systems is well motivated. Were it successful, it would imply wide-ranging applications.
Book Synopsis An Introduction to Celestial Mechanics by : Forest Ray Moulton
Download or read book An Introduction to Celestial Mechanics written by Forest Ray Moulton and published by . This book was released on 1914 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Vladimir I. Arnold - Collected Works by : Vladimir I. Arnold
Download or read book Vladimir I. Arnold - Collected Works written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2009-10-22 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vladimir Arnold is one of the greatest mathematical scientists of our time, as well as one of the finest, most prolific mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics and KAM theory.
Book Synopsis New Foundations for Classical Mechanics by : D. Hestenes
Download or read book New Foundations for Classical Mechanics written by D. Hestenes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applica tions matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.
