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Geometry, Mechanics, and Dynamics

2015-04-16 Mathematics
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Release : 2015-04-16
Genre : Mathematics
Kind : eBook
Book Rating : 419/5 ( reviews)

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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. This book was released on 2015-04-16. 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.

Geometry, Mechanics, and Dynamics

2006-05-11 Mathematics
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Release : 2006-05-11
Genre : Mathematics
Kind : eBook
Book Rating : 916/5 ( reviews)

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Book Synopsis Geometry, Mechanics, and Dynamics by : Paul Newton

Download or read book Geometry, Mechanics, and Dynamics written by Paul Newton. This book was released on 2006-05-11. Available in PDF, EPUB and Kindle. Book excerpt: Jerry Marsden, one of the world’s pre-eminent mechanicians and applied mathematicians, celebrated his 60th birthday in August 2002. The event was marked by a workshop on “Geometry, Mechanics, and Dynamics”at the Fields Institute for Research in the Mathematical Sciences, of which he wasthefoundingDirector. Ratherthanmerelyproduceaconventionalp- ceedings, with relatively brief accounts of research and technical advances presented at the meeting, we wished to acknowledge Jerry’s in?uence as a teacher, a propagator of new ideas, and a mentor of young talent. Con- quently, starting in 1999, we sought to collect articles that might be used as entry points by students interested in ?elds that have been shaped by Jerry’s work. At the same time we hoped to give experts engrossed in their own technical niches an indication of the wonderful breadth and depth of their subjects as a whole. This book is an outcome of the e?orts of those who accepted our in- tations to contribute. It presents both survey and research articles in the several ?elds that represent the main themes of Jerry’s work, including elasticity and analysis, ?uid mechanics, dynamical systems theory, g- metric mechanics, geometric control theory, and relativity and quantum mechanics. The common thread running through this broad tapestry is the use of geometric methods that serve to unify diverse disciplines and bring a widevarietyofscientistsandmathematicianstogether,speakingalanguage which enhances dialogue and encourages cross-fertilization.

Geometric Dynamics

2000 Mathematics
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Release : 2000
Genre : Mathematics
Kind : eBook
Book Rating : 016/5 ( reviews)

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Book Synopsis Geometric Dynamics by : Constantin Udriște

Download or read book Geometric Dynamics written by Constantin Udriște. This book was released on 2000. 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.

Dynamical Systems and Geometric Mechanics

2018-08-21 Science
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Release : 2018-08-21
Genre : Science
Kind : eBook
Book Rating : 802/5 ( reviews)

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Book Synopsis Dynamical Systems and Geometric Mechanics by : Jared Maruskin

Download or read book Dynamical Systems and Geometric Mechanics written by Jared Maruskin. This book was released on 2018-08-21. 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.

Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics

2007-06-14 Mathematics
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Release : 2007-06-14
Genre : Mathematics
Kind : eBook
Book Rating : 571/5 ( reviews)

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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. This book was released on 2007-06-14. 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.

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