Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature PDF Download
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Author: T.G. Vozmischeva
Publisher: Springer Science & Business Media
ISBN: 9401703035
Category : Science
Languages : en
Pages : 194
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Book Description
Introd uction The problem of integrability or nonintegrability of dynamical systems is one of the central problems of mathematics and mechanics. Integrable cases are of considerable interest, since, by examining them, one can study general laws of behavior for the solutions of these systems. The classical approach to studying dynamical systems assumes a search for explicit formulas for the solutions of motion equations and then their analysis. This approach stimulated the development of new areas in mathematics, such as the al gebraic integration and the theory of elliptic and theta functions. In spite of this, the qualitative methods of studying dynamical systems are much actual. It was Poincare who founded the qualitative theory of differential equa tions. Poincare, working out qualitative methods, studied the problems of celestial mechanics and cosmology in which it is especially important to understand the behavior of trajectories of motion, i.e., the solutions of differential equations at infinite time. Namely, beginning from Poincare systems of equations (in connection with the study of the problems of ce lestial mechanics), the right-hand parts of which don't depend explicitly on the independent variable of time, i.e., dynamical systems, are studied.
Author: T.G. Vozmischeva
Publisher: Springer Science & Business Media
ISBN: 9401703035
Category : Science
Languages : en
Pages : 194
Get Book Here
Book Description
Introd uction The problem of integrability or nonintegrability of dynamical systems is one of the central problems of mathematics and mechanics. Integrable cases are of considerable interest, since, by examining them, one can study general laws of behavior for the solutions of these systems. The classical approach to studying dynamical systems assumes a search for explicit formulas for the solutions of motion equations and then their analysis. This approach stimulated the development of new areas in mathematics, such as the al gebraic integration and the theory of elliptic and theta functions. In spite of this, the qualitative methods of studying dynamical systems are much actual. It was Poincare who founded the qualitative theory of differential equa tions. Poincare, working out qualitative methods, studied the problems of celestial mechanics and cosmology in which it is especially important to understand the behavior of trajectories of motion, i.e., the solutions of differential equations at infinite time. Namely, beginning from Poincare systems of equations (in connection with the study of the problems of ce lestial mechanics), the right-hand parts of which don't depend explicitly on the independent variable of time, i.e., dynamical systems, are studied.
Author: Şengül Kuru
Publisher: Springer
ISBN: 3030200876
Category : Science
Languages : en
Pages : 434
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Book Description
This volume shares and makes accessible new research lines and recent results in several branches of theoretical and mathematical physics, among them Quantum Optics, Coherent States, Integrable Systems, SUSY Quantum Mechanics, and Mathematical Methods in Physics. In addition to a selection of the contributions presented at the "6th International Workshop on New Challenges in Quantum Mechanics: Integrability and Supersymmetry", held in Valladolid, Spain, 27-30 June 2017, several high quality contributions from other authors are also included. The conference gathered 60 participants from many countries working in different fields of Theoretical Physics, and was dedicated to Prof. Véronique Hussin—an internationally recognized expert in many branches of Mathematical Physics who has been making remarkable contributions to this field since the 1980s. The reader will find interesting reviews on the main topics from internationally recognized experts in each field, as well as other original contributions, all of which deal with recent applications or discoveries in the aforementioned areas.
Author: Sergei Kopeikin
Publisher: John Wiley & Sons
ISBN: 3527634576
Category : Science
Languages : en
Pages : 897
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Book Description
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.
Author: Urs Frauenfelder
Publisher: Springer
ISBN: 3319722786
Category : Mathematics
Languages : en
Pages : 381
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Book Description
The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019
Author: Ron Donagi
Publisher: Cambridge University Press
ISBN: 1108715745
Category : Mathematics
Languages : en
Pages : 421
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Book Description
A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.
Author: Ron Donagi
Publisher: Cambridge University Press
ISBN: 110880358X
Category : Mathematics
Languages : en
Pages : 421
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Book Description
Created as a celebration of mathematical pioneer Emma Previato, this comprehensive book highlights the connections between algebraic geometry and integrable systems, differential equations, mathematical physics, and many other areas. The authors, many of whom have been at the forefront of research into these topics for the last decades, have all been influenced by Previato's research, as her collaborators, students, or colleagues. The diverse articles in the book demonstrate the wide scope of Previato's work and the inclusion of several survey and introductory articles makes the text accessible to graduate students and non-experts, as well as researchers. This first volume covers a wide range of areas related to integrable systems, often emphasizing the deep connections with algebraic geometry. Common themes include theta functions and Abelian varieties, Lax equations, integrable hierarchies, Hamiltonian flows and difference operators. These powerful tools are applied to spinning top, Hitchin, Painleve and many other notable special equations.
Author: D.E. Gary
Publisher: Springer Science & Business Media
ISBN: 1402028148
Category : Science
Languages : en
Pages : 414
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Book Description
This volume is the outgrowth of several international meetings to discuss a vision for the future of solar radio physics: the development of a new radio instrument. From these discussions, the concept for the Frequency Agile Solar Radiotelescope (FASR) was born. Most of the chapters of this book are based oninvitedtalksattheFASRScienceWorkshop,heldinGreenbank,WVinMay 2002, and a special session on Solar and Space Weather Radiophysics held at the 200th American Astronomical Society meeting held in Albuquerque, NM in June 2002. Although many of the chapters deal with topics of interest in planning for FASR, other topics in Solar and Space Weather Radiophysics, such as solar radar and interplanetary scintillation, are covered to round out the discipline. The authors have been asked to write with a tutorial approach, to make the book useful to graduate students and scientists new to radio physics. This book is more than a compilation of FASR science topics. The FASR instrument concept is so revolutionary—by extending capability by an order of magnitude in several dimensions at once (frequency coverage, spatial reso- tion,dynamicrange,timeresolution,polarizationprecision)—thatitchallenges scientiststothinkinnewways. Theauthorsofthefollowingchaptershavebeen taskednotonlywithreviewingthecurrentstateofthe?eld,butalsowithlooking to the future and imagining what is possible. Radio emission is extremely complex because it is generated so readily, and every imaginable plasma parameter affects it. This is both its great strength and its weakness.
Author: Arnold Hanslmeier
Publisher: Springer Science & Business Media
ISBN: 1402056044
Category : Science
Languages : en
Pages : 327
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Book Description
This book presents comprehensive coverage of the Sun and space weather, two rapidly evolving topics. In this new edition, the information has been updated to include the latest results. In addition, new sections are included, like one on space weather data sources, as well as examples and information on new satellite missions.
Author: Alexey V. Shchepetilov
Publisher: Springer
ISBN: 3540353860
Category : Science
Languages : en
Pages : 267
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Book Description
This is an introduction to classical and quantum mechanics on two-point homogenous Riemannian spaces, empahsizing spaces with constant curvature. Chapters 1-4 provide basic notations for studying two-body dynamics. Chapter 5 deals with the problem of finding explicitly invariant expressions for the two-body quantum Hamiltonian. Chapter 6 addresses one-body problems in a central potential. Chapter 7 investigates the classical counterpart of the quantum system introduced in Chapter 5. Chapter 8 discusses applications in the quantum realm.
Author: Jacques Lépine
Publisher: Springer Science & Business Media
ISBN: 1402026005
Category : Science
Languages : en
Pages : 406
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Book Description
The international colloquium Open Issues in Local Star Formation and Early Stellar Evolution was focused on: the physics of young stellar objects, which are observed with increasing angular resolution by the new generation of telescopes; and the processes that triggered large scale star formation in the solar neighbourhood. The scientific presentations were not limited to these two main topics as many new and interesting results related to star formation have been obtained.; The participants presented new findings in the fields of stellar groups and associations; young stellar objects; disks; outflows and jets; the ISM conditions for star formation; and early stages of star formation. The discussions on open issues, representing problems and unanswered questions, should make this book particularly useful for researchers and PhD students.
