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Geometry Mechanics And Dynamics
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Book Synopsis Geometry, Mechanics, and Dynamics by : Dong Eui Chang
Download or read book Geometry, Mechanics, and Dynamics written by Dong Eui Chang and published by Springer. This book was released on 2015-04-16 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates the broad range of Jerry Marsden’s mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective. Each contribution develops its material from the viewpoint of geometric mechanics beginning at the very foundations, introducing readers to modern issues via illustrations in a wide range of topics. The twenty refereed papers contained in this volume are based on lectures and research performed during the month of July 2012 at the Fields Institute for Research in Mathematical Sciences, in a program in honor of Marsden's legacy. The unified treatment of the wide breadth of topics treated in this book will be of interest to both experts and novices in geometric mechanics. Experts will recognize applications of their own familiar concepts and methods in a wide variety of fields, some of which they may never have approached from a geometric viewpoint. Novices may choose topics that interest them among the various fields and learn about geometric approaches and perspectives toward those topics that will be new for them as well.
Book Synopsis Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics by : Marco Pettini
Download or read book Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics written by Marco Pettini and published by Springer Science & Business Media. This book was released on 2007-06-14 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The author focuses on two main areas: Riemannian formulation of Hamiltonian dynamics, providing an original viewpoint about the relationship between geodesic instability and curvature properties of the mechanical manifolds; and a topological theory of thermodynamic phase transitions, relating topology changes of microscopic configuration space with the generation of singularities of thermodynamic observables. The book contains numerous illustrations throughout and it will interest both mathematicians and physicists.
Book Synopsis Geometry from Dynamics, Classical and Quantum by : José F. Cariñena
Download or read book Geometry from Dynamics, Classical and Quantum written by José F. Cariñena and published by Springer. This book was released on 2014-09-23 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'' and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and super integrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics.
Book Synopsis Geometry, Mechanics, and Control in Action for the Falling Cat by : Toshihiro Iwai
Download or read book Geometry, Mechanics, and Control in Action for the Falling Cat written by Toshihiro Iwai and published by Springer Nature. This book was released on 2021-04-23 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The falling cat is an interesting theme to pursue, in which geometry, mechanics, and control are in action together. As is well known, cats can almost always land on their feet when tossed into the air in an upside-down attitude. If cats are not given a non-vanishing angular momentum at an initial instant, they cannot rotate during their motion, and the motion they can make in the air is vibration only. However, cats accomplish a half turn without rotation when landing on their feet. In order to solve this apparent mystery, one needs to thoroughly understand rotations and vibrations. The connection theory in differential geometry can provide rigorous definitions of rotation and vibration for many-body systems. Deformable bodies of cats are not easy to treat mechanically. A feasible way to approach the question of the falling cat is to start with many-body systems and then proceed to rigid bodies and, further, to jointed rigid bodies, which can approximate the body of a cat. In this book, the connection theory is applied first to a many-body system to show that vibrational motions of the many-body system can result in rotations without performing rotational motions and then to the cat model consisting of jointed rigid bodies. On the basis of this geometric setting, mechanics of many-body systems and of jointed rigid bodies must be set up. In order to take into account the fact that cats can deform their bodies, three torque inputs which may give a twist to the cat model are applied as control inputs under the condition of the vanishing angular momentum. Then, a control is designed according to the port-controlled Hamiltonian method for the model cat to perform a half turn and to halt the motion upon landing. The book also gives a brief review of control systems through simple examples to explain the role of control inputs.
Book Synopsis Geometric Dynamics by : Constantin Udriște
Download or read book Geometric Dynamics written by Constantin Udriște and published by Springer Science & Business Media. This book was released on 2000 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theme of this text is the philosophy that any particle flow generates a particle dynamics, in a suitable geometrical framework. It covers topics that include: geometrical and physical vector fields; field lines; flows; stability of equilibrium points; potential systems and catastrophe geometry; field hypersurfaces; bifurcations; distribution orthogonal to a vector field; extrema with nonholonomic constraints; thermodynamic systems; energies; geometric dynamics induced by a vector field; magnetic fields around piecewise rectilinear electric circuits; geometric magnetic dynamics; and granular materials and their mechanical behaviour. The text should be useful for first-year graduate students in mathematics, mechanics, physics, engineering, biology, chemistry, and economics. It can also be addressed to professors and researchers whose work involves mathematics, mechanics, physics, engineering, biology, chemistry, and economics.
Book Synopsis Introduction to Differential Geometry with Applications to Navier-Stokes Dynamics by : Troy L Story
Download or read book Introduction to Differential Geometry with Applications to Navier-Stokes Dynamics written by Troy L Story and published by iUniverse. This book was released on 2005 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Differential Geometry with applications to Navier-Stokes Dynamics is an invaluable manuscript for anyone who wants to understand and use exterior calculus and differential geometry, the modern approach to calculus and geometry. Author Troy Story makes use of over thirty years of research experience to provide a smooth transition from conventional calculus to exterior calculus and differential geometry, assuming only a knowledge of conventional calculus. Introduction to Differential Geometry with applications to Navier-Stokes Dynamics includes the topics: Geometry, Exterior calculus, Homology and co-homology, Applications of differential geometry and exterior calculus to: Hamiltonian mechanics, geometric optics, irreversible thermodynamics, black hole dynamics, electromagnetism, classical string fields, and Navier-Stokes dynamics.
Book Synopsis Mechanics in Differential Geometry by : Yves Talpaert
Download or read book Mechanics in Differential Geometry written by Yves Talpaert and published by Walter de Gruyter. This book was released on 2006 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This course and reference book is autonomous and is based on differential geometry in a practical way with symplectic geometry as a tool. Didactic comparisons, diagrams, exercises highlight modern mechanics. Principles, canonical forms, perturbations, stability, qualitative dynamics, and more precede an original Fourier transforms method.
Book Synopsis The Elements of Dynamics (mechanics). by : James Blaikie
Download or read book The Elements of Dynamics (mechanics). written by James Blaikie and published by . This book was released on 1888 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Methods of Classical Mechanics by : V.I. Arnol'd
Download or read book Mathematical Methods of Classical Mechanics written by V.I. Arnol'd and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Book Synopsis Principles of Engineering Mechanics by : Millard F. Beatty
Download or read book Principles of Engineering Mechanics written by Millard F. Beatty and published by Springer Science & Business Media. This book was released on 2005-11-30 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Separation of the elements of classical mechanics into kinematics and dynamics is an uncommon tutorial approach, but the author uses it to advantage in this two-volume set. Students gain a mastery of kinematics first – a solid foundation for the later study of the free-body formulation of the dynamics problem. A key objective of these volumes, which present a vector treatment of the principles of mechanics, is to help the student gain confidence in transforming problems into appropriate mathematical language that may be manipulated to give useful physical conclusions or specific numerical results. In the first volume, the elements of vector calculus and the matrix algebra are reviewed in appendices. Unusual mathematical topics, such as singularity functions and some elements of tensor analysis, are introduced within the text. A logical and systematic building of well-known kinematic concepts, theorems, and formulas, illustrated by examples and problems, is presented offering insights into both fundamentals and applications. Problems amplify the material and pave the way for advanced study of topics in mechanical design analysis, advanced kinematics of mechanisms and analytical dynamics, mechanical vibrations and controls, and continuum mechanics of solids and fluids. Volume I of Principles of Engineering Mechanics provides the basis for a stimulating and rewarding one-term course for advanced undergraduate and first-year graduate students specializing in mechanics, engineering science, engineering physics, applied mathematics, materials science, and mechanical, aerospace, and civil engineering. Professionals working in related fields of applied mathematics will find it a practical review and a quick reference for questions involving basic kinematics.
Book Synopsis The Geometry and Dynamics of Magnetic Monopoles by : Michael Francis Atiyah
Download or read book The Geometry and Dynamics of Magnetic Monopoles written by Michael Francis Atiyah and published by Princeton University Press. This book was released on 2014-07-14 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems governed by non-linear differential equations are of fundamental importance in all branches of science, but our understanding of them is still extremely limited. In this book a particular system, describing the interaction of magnetic monopoles, is investigated in detail. The use of new geometrical methods produces a reasonably clear picture of the dynamics for slowly moving monopoles. This picture clarifies the important notion of solitons, which has attracted much attention in recent years. The soliton idea bridges the gap between the concepts of "fields" and "particles," and is here explored in a fully three-dimensional context. While the background and motivation for the work comes from physics, the presentation is mathematical. This book is interdisciplinary and addresses concerns of theoretical physicists interested in elementary particles or general relativity and mathematicians working in analysis or geometry. The interaction between geometry and physics through non-linear partial differential equations is now at a very exciting stage, and the book is a contribution to this activity. Originally published in 1988. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Book Synopsis Geometric Mechanics and Symmetry by : Darryl D. Holm
Download or read book Geometric Mechanics and Symmetry written by Darryl D. Holm and published by Oxford University Press. This book was released on 2009-07-30 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate level text based partly on lectures in geometry, mechanics, and symmetry given at Imperial College London, this book links traditional classical mechanics texts and advanced modern mathematical treatments of the subject.
Book Synopsis Symplectic Geometry and Topology by : Yakov Eliashberg
Download or read book Symplectic Geometry and Topology written by Yakov Eliashberg and published by American Mathematical Soc.. This book was released on 2004 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symplectic geometry has its origins as a geometric language for classical mechanics. But it has recently exploded into an independent field interconnected with many other areas of mathematics and physics. The goal of the IAS/Park City Mathematics Institute Graduate Summer School on Symplectic Geometry and Topology was to give an intensive introduction to these exciting areas of current research. Included in this proceedings are lecture notes from the following courses: Introductionto Symplectic Topology by D. McDuff; Holomorphic Curves and Dynamics in Dimension Three by H. Hofer; An Introduction to the Seiberg-Witten Equations on Symplectic Manifolds by C. Taubes; Lectures on Floer Homology by D. Salamon; A Tutorial on Quantum Cohomology by A. Givental; Euler Characteristicsand Lagrangian Intersections by R. MacPherson; Hamiltonian Group Actions and Symplectic Reduction by L. Jeffrey; and Mechanics: Symmetry and Dynamics by J. Marsden. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
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 Nonholonomic Mechanics and Control by : A.M. Bloch
Download or read book Nonholonomic Mechanics and Control written by A.M. Bloch and published by Springer Science & Business Media. This book was released on 2008-02-03 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores connections between control theory and geometric mechanics. The author links control theory with a geometric view of classical mechanics in both its Lagrangian and Hamiltonian formulations, and in particular with the theory of mechanical systems subject to motion constraints. The synthesis is appropriate as there is a rich connection between mechanics and nonlinear control theory. The book provides a unified treatment of nonlinear control theory and constrained mechanical systems that incorporates material not available in other recent texts. The book benefits graduate students and researchers in the area who want to enhance their understanding and enhance their techniques.
Book Synopsis Non-relativistic Quantum Theory: Dynamics, Symmetry And Geometry by : Kai S Lam
Download or read book Non-relativistic Quantum Theory: Dynamics, Symmetry And Geometry written by Kai S Lam and published by World Scientific Publishing Company. This book was released on 2009-08-24 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is mainly for physics students at the advanced undergraduate and beginning graduate levels, especially those with a theoretical inclination. Its chief purpose is to give a systematic introduction to the main ingredients of the fundamentals of quantum theory, with special emphasis on those aspects of group theory (spacetime and permutational symmetries and group representations) and differential geometry (geometrical phases, topological quantum numbers, and Chern-Simons Theory) that are relevant in modern developments of the subject. It will provide students with an overview of key elements of the theory, as well as a solid preparation in calculational techniques.
Book Synopsis Geometry, Topology, and Dynamics in Negative Curvature by : C. S. Aravinda
Download or read book Geometry, Topology, and Dynamics in Negative Curvature written by C. S. Aravinda and published by Cambridge University Press. This book was released on 2016-01-21 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.
