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Space Manifold Dynamics

2010-07-23 Science
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Release : 2010-07-23
Genre : Science
Kind : eBook
Book Rating : 488/5 ( reviews)

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Book Synopsis Space Manifold Dynamics by : Ettore Perozzi

Download or read book Space Manifold Dynamics written by Ettore Perozzi. This book was released on 2010-07-23. 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.

Dynamics On Lorentz Manifolds

2001-11-19 Science
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Release : 2001-11-19
Genre : Science
Kind : eBook
Book Rating : 620/5 ( reviews)

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Book Synopsis Dynamics On Lorentz Manifolds by : Scot Adams

Download or read book Dynamics On Lorentz Manifolds written by Scot Adams. This book was released on 2001-11-19. 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.

Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds

2017-08-14 Mathematics
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Release : 2017-08-14
Genre : Mathematics
Kind : eBook
Book Rating : 538/5 ( reviews)

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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. This book was released on 2017-08-14. 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.

Invariant Manifolds in Discrete and Continuous Dynamical Systems

2013 Banach spaces
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Release : 2013
Genre : Banach spaces
Kind : eBook
Book Rating : 243/5 ( reviews)

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Book Synopsis Invariant Manifolds in Discrete and Continuous Dynamical Systems by : Kaspar Nipp

Download or read book Invariant Manifolds in Discrete and Continuous Dynamical Systems written by Kaspar Nipp. This book was released on 2013. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Differential Geometry Applied to Dynamical Systems

2009 Science
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Release : 2009
Genre : Science
Kind : eBook
Book Rating : 150/5 ( reviews)

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Book Synopsis Differential Geometry Applied to Dynamical Systems by : Jean-Marc Ginoux

Download or read book Differential Geometry Applied to Dynamical Systems written by Jean-Marc Ginoux. This book was released on 2009. 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 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.

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