Unstable Orbits
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Low Energy Flight Orbital Dynamics And Mission Trajectory Design
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Author : Jianping Yuan
language : en
Publisher: Springer
Release Date : 2019-03-19
Low Energy Flight Orbital Dynamics And Mission Trajectory Design written by Jianping Yuan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-19 with Technology & Engineering categories.
The book focuses on the orbital dynamics and mission trajectory (transfer or target trajectory) design of low-energy flight in the context of modern astrodynamics. It investigates various topics that either offer new methods for solving classical problems or address emerging problems that have yet to be studied, including low-thrust transfer trajectory design using the virtual gravity field method; transfer in the three-body system using invariant manifolds; formation flying under space-borne artificial magnetic fields; and the orbital dynamics of highly irregular asteroids. It also features an extensive study of the orbital dynamics in the vicinity of contact binary asteroids, including the 1:1 ground-track resonance, the equilibrium points and their stability, and the third-order analytical solution of orbital motion in the vicinity of the non-collinear equilibrium point. Given its breadth of coverage, the book offers a valuable reference guide for allengineers and researchers interested in the potential applications of low-energy space missions.
Chaos
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Author : Kathleen Alligood
language : en
Publisher: Springer
Release Date : 2012-12-06
Chaos written by Kathleen Alligood and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
BACKGROUND Sir Isaac Newton hrought to the world the idea of modeling the motion of physical systems with equations. It was necessary to invent calculus along the way, since fundamental equations of motion involve velocities and accelerations, of position. His greatest single success was his discovery that which are derivatives the motion of the planets and moons of the solar system resulted from a single fundamental source: the gravitational attraction of the hodies. He demonstrated that the ohserved motion of the planets could he explained hy assuming that there is a gravitational attraction he tween any two ohjects, a force that is proportional to the product of masses and inversely proportional to the square of the distance between them. The circular, elliptical, and parabolic orhits of astronomy were v INTRODUCTION no longer fundamental determinants of motion, but were approximations of laws specified with differential equations. His methods are now used in modeling motion and change in all areas of science. Subsequent generations of scientists extended the method of using differ ential equations to describe how physical systems evolve. But the method had a limitation. While the differential equations were sufficient to determine the behavior-in the sense that solutions of the equations did exist-it was frequently difficult to figure out what that behavior would be. It was often impossible to write down solutions in relatively simple algebraic expressions using a finite number of terms. Series solutions involving infinite sums often would not converge beyond some finite time.
Introduction To Discrete Dynamical Systems And Chaos
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Author : Mario Martelli
language : en
Publisher: John Wiley & Sons
Release Date : 2011-11-01
Introduction To Discrete Dynamical Systems And Chaos written by Mario Martelli and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-01 with Mathematics categories.
A timely, accessible introduction to the mathematics of chaos. The past three decades have seen dramatic developments in the theory of dynamical systems, particularly regarding the exploration of chaotic behavior. Complex patterns of even simple processes arising in biology, chemistry, physics, engineering, economics, and a host of other disciplines have been investigated, explained, and utilized. Introduction to Discrete Dynamical Systems and Chaos makes these exciting and important ideas accessible to students and scientists by assuming, as a background, only the standard undergraduate training in calculus and linear algebra. Chaos is introduced at the outset and is then incorporated as an integral part of the theory of discrete dynamical systems in one or more dimensions. Both phase space and parameter space analysis are developed with ample exercises, more than 100 figures, and important practical examples such as the dynamics of atmospheric changes and neural networks. An appendix provides readers with clear guidelines on how to use Mathematica to explore discrete dynamical systems numerically. Selected programs can also be downloaded from a Wiley ftp site (address in preface). Another appendix lists possible projects that can be assigned for classroom investigation. Based on the author's 1993 book, but boasting at least 60% new, revised, and updated material, the present Introduction to Discrete Dynamical Systems and Chaos is a unique and extremely useful resource for all scientists interested in this active and intensely studied field.
Working With Dynamical Systems
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Author : Len Pismen
language : en
Publisher: CRC Press
Release Date : 2020-12-15
Working With Dynamical Systems written by Len Pismen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-15 with Mathematics categories.
This book provides working tools for the study and design of nonlinear dynamical systems applicable in physics and engineering. It offers a broad-based introduction to this challenging area of study, taking an applications-oriented approach that emphasizes qualitative analysis and approximations rather than formal mathematics or simulation. The author, an internationally recognized authority in the field, makes extensive use of examples and includes executable Mathematica notebooks that may be used to generate new examples as hands-on exercises. The coverage includes discussion of mechanical models, chemical and ecological interactions, nonlinear oscillations and chaos, forcing and synchronization, spatial patterns and waves. Key Features: · Written for a broad audience, avoiding dependence on mathematical formulations in favor of qualitative, constructive treatment. · Extensive use of physical and engineering applications. · Incorporates Mathematica notebooks for simulations and hands-on self-study. · Provides a gentle but rigorous introduction to real-world nonlinear problems. · Features a final chapter dedicated to applications of dynamical systems to spatial patterns. The book is aimed at student and researchers in applied mathematics and mathematical modelling of physical and engineering problems. It teaches to see common features in systems of different origins, and to apply common methods of study without losing sight of complications and uncertainties related to their physical origin.
Lagrangian Oceanography
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Author : Sergey V. Prants
language : en
Publisher: Springer
Release Date : 2017-03-27
Lagrangian Oceanography written by Sergey V. Prants and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-27 with Science categories.
This book uses the Lagrangian approach, especially useful and convenient for studying large-scale transport and mixing in the ocean, to present a detailed view of ocean circulation. This approach focuses on simulations and on monitoring the trajectories of fluid particles, which are governed by advection equations. The first chapter of the book is devoted to dynamical systems theory methods, which provide the framework, methodology and key concepts for the Lagrangian approach. The book then moves on to an analysis of chaotic mixing and cross-stream transport in idealized models of oceanic meandering currents like the Gulfstream in the Atlantic, the Kuroshio in the Pacific, and Antarctic Circumpolar Current, after which the current state of physical oceanography is reviewed. The latter half of the book applies the techniques and methods already described in order to study eddies, currents, fronts and large-scale mixing and transport in the Far-Eastern seas and the north-western part of the Pacific Ocean. Finally, the book concludes with a discussion of Lagrangian simulation and monitoring of water contamination after the Fukushima disaster of 2011. The propagation of Fukushima-derived radionuclides, surface transport across the Kuroshio Extension current, and the role of mesoscale eddies in the transport of Fukushima-derived cesium isotopes in the ocean are examined, and a comparison of simulation results with actual measurements are presented.Written by some of the world leaders in the application of Lagrangian methods in oceanography, this title will be of benefit to the oceanographic community by presenting the necessary background of the Lagrangian approach in an accessible manner.
Spacecraft Dynamics And Control
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Author : Yongchun Xie
language : en
Publisher: Springer Nature
Release Date : 2021-07-13
Spacecraft Dynamics And Control written by Yongchun Xie and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-13 with Technology & Engineering categories.
This book presents up-to-date concepts and design methods relating to space dynamics and control, including spacecraft attitude control, orbit control, and guidance, navigation, and control (GNC), summarizing the research advances in control theory and methods and engineering practice from Beijing Institute of Control Engineering over the years. The control schemes and systems based on these achievements have been successfully applied to remote sensing satellites, communication satellites, navigation satellites, new technology test satellites, Shenzhou manned spacecraft, Tianzhou freight spacecraft, Tiangong 1/2 space laboratories, Chang'e lunar explorers, and many other missions. Further, the research serves as a guide for follow-up engineering developments in manned lunar engineering, deep space exploration, and on-orbit service missions.
Advances In Astronomy And Astrophysics
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Author : Zdeněk Kopal
language : en
Publisher: Academic Press
Release Date : 2013-10-22
Advances In Astronomy And Astrophysics written by Zdeněk Kopal and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.
Advances in Astronomy and Astrophysics, Volume 6 brings together numerous research works on different aspects of astronomy and astrophysics. This volume is composed of five chapters, and starts with the description of improved methods for analyzing and classifying families of periodic orbits in a conservative dynamical system with two degrees of freedom. The next chapter describes the variation of fractional luminosity of distorted components of close binary systems in the course of their revolution, or the accompanying changes in radial velocity. This topic is followed by discussions on various mechanisms that have been proposed for the interstellar medium, as well as the mass exchange and evolution of close binary stars. The concluding chapter examines evidence for lunar luminescence. This book will prove useful to astronomers and astrophysicists.
A Comparison Of The Dynamical Evolution Of Planetary Systems
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Author : Rudolf Dvorak
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-16
A Comparison Of The Dynamical Evolution Of Planetary Systems written by Rudolf Dvorak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Science categories.
The papers in this volume cover a wide range of subjects covering the most recent developments in Celestial Mechanics from the theoretical point of nonlinear dynamical systems to the application to real problems. We emphasize the papers on the formation of planetary systems, their stability and also the problem of habitable zones in extrasolar planetary systems. A special topic is the stability of Trojans in our planetary system, where more and more realistic dynamical models are used to explain their complex motions: besides the important contribution from the theoretical point of view, the results of several numerical experiments unraveled the structure of the stable zone around the librations points. This volume will be of interest to astronomers and mathematicians interested in Hamiltonian mechanics and in the dynamics of planetary systems.
Semiclassical Physics
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Author : Matthias Brack
language : en
Publisher: CRC Press
Release Date : 2018-03-05
Semiclassical Physics written by Matthias Brack and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-05 with Science categories.
This book attempts to convey to the reader that semiclassical physics can be fun, as well as useful for understanding quantum fluctuations in interacting many-body systems. It presents applications to finite fermion systems in diverse areas of physics.
Hamiltonian Systems With Three Or More Degrees Of Freedom
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Author : Carles Simó
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Hamiltonian Systems With Three Or More Degrees Of Freedom written by Carles Simó and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schrödinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions.