Geometric Mechanics

Geometric Mechanics
Author: Richard Talman
Publisher: Wiley-VCH
Total Pages: 592
Release: 2000
Genre: Mathematics
ISBN:

Not just another book on mechanics, Geometric Mechanics sets itself apart in important ways. It offers a modern treatment of classical mechanics, including material on relativistic physics, chaos theory, and nonlinear dynamics in addition to standard topics.

Geometric Mechanics on Riemannian Manifolds

Geometric Mechanics on Riemannian Manifolds
Author: Ovidiu Calin
Publisher: Springer Science & Business Media
Total Pages: 285
Release: 2006-03-15
Genre: Mathematics
ISBN: 0817644210

* A geometric approach to problems in physics, many of which cannot be solved by any other methods * Text is enriched with good examples and exercises at the end of every chapter * Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics

Symplectic Geometry and Analytical Mechanics

Symplectic Geometry and Analytical Mechanics
Author: P. Libermann
Publisher: Springer Science & Business Media
Total Pages: 541
Release: 2012-12-06
Genre: Mathematics
ISBN: 9400938071

Approach your problems from the right end It isn't that they can't see the solution. and begin with the answers. Then one day, It is that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' Brown 'The point of a Pin'. in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thouglit to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sci ences has changed drastically in recent years: measure theory is used (non-trivially) in re gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homo topy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

Geometric Continuum Mechanics

Geometric Continuum Mechanics
Author: Reuven Segev
Publisher: Springer Nature
Total Pages: 416
Release: 2020-05-13
Genre: Mathematics
ISBN: 3030426831

This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include: Global stress and hyper-stress theories Applications of de Rham currents to singular dislocations Manifolds of mappings for continuum mechanics Kinematics of defects in solid crystals Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.

Geometry, Mechanics, and Dynamics

Geometry, Mechanics, and Dynamics
Author: Dong Eui Chang
Publisher: Springer
Total Pages: 506
Release: 2015-04-16
Genre: Mathematics
ISBN: 1493924419

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.

Geometric Control of Mechanical Systems

Geometric Control of Mechanical Systems
Author: Francesco Bullo
Publisher: Springer
Total Pages: 741
Release: 2019-06-12
Genre: Science
ISBN: 1489972765

The area of analysis and control of mechanical systems using differential geometry is flourishing. This book collects many results over the last decade and provides a comprehensive introduction to the area.

Mechanics, Analysis and Geometry: 200 Years after Lagrange

Mechanics, Analysis and Geometry: 200 Years after Lagrange
Author: M. Francaviglia
Publisher: Elsevier
Total Pages: 572
Release: 2012-12-02
Genre: Science
ISBN: 0444597379

Providing a logically balanced and authoritative account of the different branches and problems of mathematical physics that Lagrange studied and developed, this volume presents up-to-date developments in differential goemetry, dynamical systems, the calculus of variations, and celestial and analytical mechanics.

Mathematical Methods of Classical Mechanics

Mathematical Methods of Classical Mechanics
Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
Total Pages: 530
Release: 2013-04-09
Genre: Mathematics
ISBN: 1475720637

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.

Geometric Mechanics and Symmetry

Geometric Mechanics and Symmetry
Author: Darryl D. Holm
Publisher: Oxford University Press
Total Pages: 537
Release: 2009-07-30
Genre: Mathematics
ISBN: 0199212902

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.

Geometric Mechanics: Dynamics and symmetry

Geometric Mechanics: Dynamics and symmetry
Author: Darryl D. Holm
Publisher: Imperial College Press
Total Pages: 375
Release: 2008-01-01
Genre: Mathematics
ISBN: 1848161956

Advanced undergraduate and graduate students in mathematics, physics and engineering.