Space Manifold Dynamics

Author : Ettore Perozzi,Sylvio Ferraz-Mello
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 44,7 Mb
Release : 2010-07-23
Category : Science
ISBN : 9781441903488

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Space Manifold Dynamics by Ettore Perozzi,Sylvio Ferraz-Mello Pdf

This book presents an overview of the outcomes resulting from applying the dynamical systems approach to space mission design, a topic referred to as "Space Manifold Dynamics" (SMD). It is a natural follow-on to the international workshop "Novel Spaceways for Scientific and Exploration Missions," which was held in October 2007 at the Telespazio Fucino Space Centre (Italy) under the auspices of the Space OPS Academy. The benefits and drawbacks of using the Lagrangian points and the associated trajectories for present and future space missions are discussed. The related methods and algorithms are also described in detail. Each topic is presented in articles that were written as far as possible to be self consistent; the use of introductory sections and of extended explanations is included in order to address the different communities potentially interested in SMD: space science, the aerospace industry, manned and unmanned exploration, celestial mechanics, and flight dynamics.

Author : Sergei Yu. Pilyugin
Publisher : Walter de Gruyter GmbH & Co KG
Page : 379 pages
File Size : 52,6 Mb
Release : 2019-08-05
Category : Science
ISBN : 9783110653991

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Spaces of Dynamical Systems by Sergei Yu. Pilyugin Pdf

Author : Scot Adams
Publisher : World Scientific
Page : 418 pages
File Size : 47,7 Mb
Release : 2001-11-19
Category : Science
ISBN : 9789814492621

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Dynamics On Lorentz Manifolds by Scot Adams Pdf

Within the general framework of the dynamics of “large” groups on geometric spaces, the focus is on the types of groups that can act in complicated ways on Lorentz manifolds, and on the structure of the resulting manifolds and actions. This particular area of dynamics is an active one, and not all the results are in their final form. However, at this point, a great deal can be said about the particular Lie groups that come up in this context. It is impressive that, even assuming very weak recurrence of the action, the list of possible groups is quite restricted. For the most complicated of these groups, one can also describe reasonably well the local structure of the actions that arise.This advanced text is also appropriate to a course for mathematics graduate students who have completed their first year of study.

Author : Stephen Wiggins
Publisher : Springer Science & Business Media
Page : 198 pages
File Size : 50,6 Mb
Release : 2013-11-22
Category : Mathematics
ISBN : 9781461243120

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Normally Hyperbolic Invariant Manifolds in Dynamical Systems by Stephen Wiggins Pdf

In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications.

Author : Kaspar Nipp,Daniel Stoffer
Publisher : Unknown
Page : 216 pages
File Size : 55,5 Mb
Release : 2013
Category : Banach spaces
ISBN : 3037196246

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Invariant Manifolds in Discrete and Continuous Dynamical Systems by Kaspar Nipp,Daniel Stoffer Pdf

In this book, dynamical systems are investigated from a geometric viewpoint. Admitting an invariant manifold is a strong geometric property of a dynamical system. This text presents rigorous results on invariant manifolds and gives examples of possible applications. In the first part, discrete dynamical systems in Banach spaces are considered. Results on the existence and smoothness of attractive and repulsive invariant manifolds are derived. In addition, perturbations and approximations of the manifolds and the foliation of the adjacent space are treated. In the second part, analogous results for continuous dynamical systems in finite dimensions are established. In the third part, the theory developed is applied to problems in numerical analysis and to singularly perturbed systems of ordinary differential equations. The mathematical approach is based on the so-called graph transform, already used by Hadamard in 1901. The aim is to establish invariant manifold results in a simple setting that provides quantitative estimates. The book is targeted at researchers in the field of dynamical systems interested in precise theorems that are easy to apply. The application part might also serve as an underlying text for a student seminar in mathematics. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Author : Jean-Marc Ginoux
Publisher : World Scientific
Page : 341 pages
File Size : 47,9 Mb
Release : 2009
Category : Science
ISBN : 9789814277150

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Differential Geometry Applied to Dynamical Systems by Jean-Marc Ginoux Pdf

This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory OCo or the flow OCo may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes). In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem.

Author : Viacheslav Z. Grines,Timur V. Medvedev,Olga V. Pochinka
Publisher : Springer
Page : 295 pages
File Size : 54,6 Mb
Release : 2016-11-11
Category : Mathematics
ISBN : 9783319448473

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Dynamical Systems on 2- and 3-Manifolds by Viacheslav Z. Grines,Timur V. Medvedev,Olga V. Pochinka Pdf

This book provides an introduction to the topological classification of smooth structurally stable diffeomorphisms on closed orientable 2- and 3-manifolds.The topological classification is one of the main problems of the theory of dynamical systems and the results presented in this book are mostly for dynamical systems satisfying Smale's Axiom A. The main results on the topological classification of discrete dynamical systems are widely scattered among many papers and surveys. This book presents these results fluidly, systematically, and for the first time in one publication. Additionally, this book discusses the recent results on the topological classification of Axiom A diffeomorphisms focusing on the nontrivial effects of the dynamical systems on 2- and 3-manifolds. The classical methods and approaches which are considered to be promising for the further research are also discussed.“br> The reader needs to be familiar with the basic concepts of the qualitative theory of dynamical systems which are presented in Part 1 for convenience. The book is accessible to ambitious undergraduates, graduates, and researchers in dynamical systems and low dimensional topology. This volume consists of 10 chapters; each chapter contains its own set of references and a section on further reading. Proofs are presented with the exact statements of the results. In Chapter 10 the authors briefly state the necessary definitions and results from algebra, geometry and topology. When stating ancillary results at the beginning of each part, the authors refer to other sources which are readily available.

Author : Taeyoung Lee,Melvin Leok,N. Harris McClamroch
Publisher : Springer
Page : 539 pages
File Size : 41,7 Mb
Release : 2017-08-14
Category : Mathematics
ISBN : 9783319569536

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Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds by Taeyoung Lee,Melvin Leok,N. Harris McClamroch Pdf

This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.

Author : J.M. Souriau
Publisher : Springer Science & Business Media
Page : 427 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461202813

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Structure of Dynamical Systems by J.M. Souriau Pdf

The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization.

Author : Wang Sang Koon,Martin W. Lo,Jerrold E. Marsden
Publisher : Springer
Page : 336 pages
File Size : 46,5 Mb
Release : 2011-06-01
Category : Mathematics
ISBN : 0387495150

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Dynamical Systems by Wang Sang Koon,Martin W. Lo,Jerrold E. Marsden Pdf

This book considers global solutions to the restricted three-body problem from a geometric point of view. The authors seek dynamical channels in the phase space which wind around the planets and moons and naturally connect them. These low energy passageways could slash the amount of fuel spacecraft need to explore and develop our solar system. In order to effectively exploit these passageways, the book addresses the global transport. It goes beyond the traditional scope of libration point mission design, developing tools for the design of trajectories which take full advantage of natural three or more body dynamics, thereby saving precious fuel and gaining flexibility in mission planning. This is the key for the development of some NASA mission trajectories, such as low energy libration point orbit missions (e.g., the sample return Genesis Discovery Mission), low energy lunar missions and low energy tours of outer planet moon systems, such as a mission to tour and explore in detail the icy moons of Jupiter. This book can serve as a valuable resource for graduate students and advanced undergraduates in applied mathematics and aerospace engineering, as well as a manual for practitioners who work on libration point and deep space missions in industry and at government laboratories. the authors include a wealth of background material, but also bring the reader up to a portion of the research frontier.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 55,9 Mb
Release : 2024-06-02
Category : Electronic
ISBN : 9789814467636

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Differential Geometry Applied to Dynamical Systems by Anonim Pdf

Author : H. Broer,F. Takens,B. Hasselblatt
Publisher : Elsevier
Page : 560 pages
File Size : 40,9 Mb
Release : 2010-11-10
Category : Mathematics
ISBN : 0080932266

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Handbook of Dynamical Systems by H. Broer,F. Takens,B. Hasselblatt Pdf

In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems Highlights developments that are the foundation for future research in this field Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems

Author : Boling Guo,Liming Ling,Yansheng Ma,Hui Yang
Publisher : Walter de Gruyter GmbH & Co KG
Page : 438 pages
File Size : 50,8 Mb
Release : 2018-07-09
Category : Mathematics
ISBN : 9783110549652

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Attractors and Inertial Manifolds by Boling Guo,Liming Ling,Yansheng Ma,Hui Yang Pdf

This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the first volume is on the mathematical analysis of attractors and inertial manifolds. This volume deals with the existence of global attractors, inertial manifolds and with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution equations in modern physics. Known as well as many new results about the existence, regularity and properties of inertial manifolds and approximate inertial manifolds are also presented in the first volume. The second volume will be devoted to modern analytical tools and methods in infinite-dimensional dynamical systems. Contents Attractor and its dimension estimation Inertial manifold The approximate inertial manifold

Author : Giulio Baù,Alessandra Celletti,Cătălin Bogdan Galeș,Giovanni Federico Gronchi
Publisher : Springer Nature
Page : 328 pages
File Size : 50,9 Mb
Release : 2019-09-06
Category : Mathematics
ISBN : 9783030206338

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Satellite Dynamics and Space Missions by Giulio Baù,Alessandra Celletti,Cătălin Bogdan Galeș,Giovanni Federico Gronchi Pdf

This book discusses the design of new space missions and their use for a better understanding of the dynamical behaviour of solar system bodies, which is an active field of astrodynamics. Space missions gather data and observations that enable new breakthroughs in our understanding of the origin, evolution and future of our solar system and Earth’s place within it. Covering topics such as satellite and space mission dynamics, celestial mechanics, spacecraft navigation, space exploration applications, artificial satellites, space debris, minor bodies, and tidal evolution, the book presents a collection of contributions given by internationally respected scientists at the summer school “Satellite Dynamics and Space Missions: Theory and Applications of Celestial Mechanics”, held in 2017 at San Martino al Cimino, Viterbo (Italy). This school aimed to teach the latest theories, tools and methods developed for satellite dynamics and space, and as such the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.

Author : Scot Adams
Publisher : World Scientific
Page : 418 pages
File Size : 41,7 Mb
Release : 2001
Category : Science
ISBN : 9789810243821

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Dynamics on Lorentz Manifolds by Scot Adams Pdf

Within the general framework of the dynamics of ?large? groups on geometric spaces, the focus is on the types of groups that can act in complicated ways on Lorentz manifolds, and on the structure of the resulting manifolds and actions. This particular area of dynamics is an active one, and not all the results are in their final form. However, at this point, a great deal can be said about the particular Lie groups that come up in this context. It is impressive that, even assuming very weak recurrence of the action, the list of possible groups is quite restricted. For the most complicated of these groups, one can also describe reasonably well the local structure of the actions that arise.This advanced text is also appropriate to a course for mathematics graduate students who have completed their first year of study.