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Space Manifold Dynamics
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Book Synopsis Space Manifold Dynamics by : Ettore Perozzi
Download or read book Space Manifold Dynamics written by Ettore Perozzi and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds by : Taeyoung Lee
Download or read book Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds written by Taeyoung Lee and published by Springer. This book was released on 2017-08-14 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dynamical Systems by : Wang Sang Koon
Download or read book Dynamical Systems written by Wang Sang Koon and published by Springer. This book was released on 2011-06-01 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dynamics on Lorentz Manifolds by : Scot Adams
Download or read book Dynamics on Lorentz Manifolds written by Scot Adams and published by World Scientific. This book was released on 2001 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Differential Geometry Applied To Dynamical Systems (With Cd-rom) by : Jean-marc Ginoux
Download or read book Differential Geometry Applied To Dynamical Systems (With Cd-rom) written by Jean-marc Ginoux and published by World Scientific. This book was released on 2009-04-03 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 — or the flow — 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.
Book Synopsis Foliations and the Geometry of 3-Manifolds by : Danny Calegari
Download or read book Foliations and the Geometry of 3-Manifolds written by Danny Calegari and published by Oxford University Press on Demand. This book was released on 2007-05-17 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Book Synopsis Differential Dynamical Systems, Revised Edition by : James D. Meiss
Download or read book Differential Dynamical Systems, Revised Edition written by James D. Meiss and published by SIAM. This book was released on 2017-01-24 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.
Book Synopsis Manifolds, Tensor Analysis, and Applications by : Ralph Abraham
Download or read book Manifolds, Tensor Analysis, and Applications written by Ralph Abraham and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:;J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.
Book Synopsis Normally Hyperbolic Invariant Manifolds in Dynamical Systems by : Stephen Wiggins
Download or read book Normally Hyperbolic Invariant Manifolds in Dynamical Systems written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometrical Dynamics of Complex Systems by : Vladimir G. Ivancevic
Download or read book Geometrical Dynamics of Complex Systems written by Vladimir G. Ivancevic and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 842 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometrical Dynamics of Complex Systems is a graduate?level monographic textbook. Itrepresentsacomprehensiveintroductionintorigorousgeometrical dynamicsofcomplexsystemsofvariousnatures. By?complexsystems?,inthis book are meant high?dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a uni?ed geometrical - proachtodynamicsofcomplexsystemsofvariouskinds:engineering,physical, biophysical, psychophysical, sociophysical, econophysical, etc. As their names suggest, all these multi?input multi?output (MIMO) systems have something in common: the underlying physics. However, instead of dealing with the pop- 1 ular ?soft complexity philosophy?, we rather propose a rigorous geometrical and topological approach. We believe that our rigorous approach has much greater predictive power than the soft one. We argue that science and te- nology is all about prediction and control. Observation, understanding and explanation are important in education at undergraduate level, but after that it should be all prediction and control. The main objective of this book is to show that high?dimensional nonlinear systems and processes of ?real life? can be modelled and analyzed using rigorous mathematics, which enables their complete predictability and controllability, as if they were linear systems. It is well?known that linear systems, which are completely predictable and controllable by de?nition ? live only in Euclidean spaces (of various - mensions). They are as simple as possible, mathematically elegant and fully elaborated from either scienti?c or engineering side. However, in nature, no- ing is linear. In reality, everything has a certain degree of nonlinearity, which means: unpredictability, with subsequent uncontrollability.
Book Synopsis Model Emergent Dynamics in Complex Systems by : A. J. Roberts
Download or read book Model Emergent Dynamics in Complex Systems written by A. J. Roberts and published by SIAM. This book was released on 2014-12-18 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arising out of the growing interest in and applications of modern dynamical systems theory, this book explores how to derive relatively simple dynamical equations that model complex physical interactions. The author?s objectives are to use sound theory to explore algebraic techniques, develop interesting applications, and discover general modeling principles. Model Emergent Dynamics in Complex Systems unifies into one powerful and coherent approach the many varied extant methods for mathematical model reduction and approximation. Using mathematical models at various levels of resolution and complexity, the book establishes the relationships between such multiscale models and clarifying difficulties and apparent paradoxes and addresses model reduction for systems, resolves initial conditions, and illuminates control and uncertainty. The basis for the author?s methodology is the theory and the geometric picture of both coordinate transforms and invariant manifolds in dynamical systems; in particular, center and slow manifolds are heavily used. The wonderful aspect of this approach is the range of geometric interpretations of the modeling process that it produces?simple geometric pictures inspire sound methods of analysis and construction. Further, pictures drawn of state spaces also provide a route to better assess a model?s limitations and strengths. Geometry and algebra form a powerful partnership and coordinate transforms and manifolds provide a powerfully enhanced and unified view of a swathe of other complex system modeling methodologies such as averaging, homogenization, multiple scales, singular perturbations, two timing, and WKB theory.
Book Synopsis Renormalization and 3-manifolds which Fiber Over the Circle by : Curtis T. McMullen
Download or read book Renormalization and 3-manifolds which Fiber Over the Circle written by Curtis T. McMullen and published by Princeton University Press. This book was released on 1996-07-28 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many parallels between complex dynamics and hyperbolic geometry have emerged in the past decade. Building on work of Sullivan and Thurston, this book gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. Both subjects are studied via geometric limits and rigidity. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity. In complex dynamics, it motivates the construction of towers of quadratic-like maps, and leads to a quantitative proof of convergence of renormalization.
Book Synopsis Natural Biodynamics by : Vladimir G. Ivancevic
Download or read book Natural Biodynamics written by Vladimir G. Ivancevic and published by World Scientific. This book was released on 2005 with total page 1036 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive volume is a graduate-level text in human biodynamics, written in the unified categorical language of modern differential geometry and topology. Combining mathematics, physics and robotics with human physiology, this is the first book that describes all levels of human biodynamics, from musculo-skeletal mechanics to the higher brain functions. The book develops and uses a variety of research methods, ranging from chaos theory and Haken's synergetics, through quantum mechanics, to nonlinear control and artificial intelligence, to provide the means to understand, predict and control the behavior of human-like systems in their full neuro-musculo-skeletal complexity. The applications of this unique scientific methodology range from prediction of human neuro-musculo-skeletal injuries to brain-like control of humanoid robots.
Book Synopsis Dynamical Systems and Geometric Mechanics by : Jared Maruskin
Download or read book Dynamical Systems and Geometric Mechanics written by Jared Maruskin and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-08-21 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.
Book Synopsis Advanced Dynamics Modeling, Duality and Control of Robotic Systems by : Edward Y.L. Gu
Download or read book Advanced Dynamics Modeling, Duality and Control of Robotic Systems written by Edward Y.L. Gu and published by CRC Press. This book was released on 2021-09-23 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides detailed fundamental theoretical reviews and preparations necessary for developing advanced dynamics modeling and control strategies for various types of robotic systems. This research book specifically addresses and discusses the uniqueness issue of representing orientation or rotation, and further proposes an innovative isometric embedding approach. The novel approach can not only reduce the dynamic formulation for robotic systems into a compact form, but it also offers a new way to realize the orientational trajectory-tracking control procedures. In addition, the book gives a comprehensive introduction to fundamentals of mathematics and physics that are required for modeling robot dynamics and developing effective control algorithms. Many computer simulations and realistic 3D animations to verify the new theories and algorithms are included in the book as well. It also presents and discusses the principle of duality involved in robot kinematics, statics, and dynamics. The duality principle can guide the dynamics modeling and analysis into a right direction for a variety of robotic systems in different types from open serial-chain to closed parallel-chain mechanisms. It intends to serve as a diversified research reference to a wide range of audience, including undergraduate juniors and seniors, graduate students, researchers, and engineers interested in the areas of robotics, control and applications.
Download or read book Astronautics written by Ulrich Walter and published by Springer. This book was released on 2019-02-14 with total page 851 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text covers all the key concepts, relationships, and ideas behind spaceflight and is the perfect companion for students pursuing courses on or related to astronautics. As a crew member of the STS-55 Space Shuttle mission and a full professor of astronautics at the Technical University of Munich, Ulrich Walter is an acknowledged expert in the field. This book is based on his extensive teaching and work with students, and the text is backed up by numerous examples drawn from his own experience. With its end-of-chapter examples and problems, this work is suitable for graduate level or even undergraduate courses in spaceflight, as well as for professionals working in the space industry. This third edition includes substantial revisions of several sections to extend their coverage. These include both theoretical extensions such as the study of relative motion in near-circular orbits, and more practical matters such as additional details about jet-engine and general rocket performance. New sections address regularized equations of orbital motion and their algebraic solutions and also state vector propagation; two new chapters are devoted to orbit geometry and orbit determination and to thermal radiation physics and modelling.
Book Synopsis Chaotic Transport in Dynamical Systems by : Stephen Wiggins
Download or read book Chaotic Transport in Dynamical Systems written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a new and more realistic framework for describing the dynamics of non-linear systems. A number of issues arising in applied dynamical systems from the viewpoint of problems of phase space transport are raised in this monograph. Illustrating phase space transport problems arising in a variety of applications that can be modeled as time-periodic perturbations of planar Hamiltonian systems, the book begins with the study of transport in the associated two-dimensional Poincaré Map. This serves as a starting point for the further motivation of the transport issues through the development of ideas in a non-perturbative framework with generalizations to higher dimensions as well as more general time dependence. A timely and important contribution to those concerned with the applications of mathematics.
