Lagrangian Reduction By Stages PDF Download
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Author | : Hernán Cendra |
Publisher | : American Mathematical Soc. |
Total Pages | : 125 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821827154 |
Download Lagrangian Reduction by Stages Book in PDF, ePub and Kindle
This booklet studies the geometry of the reduction of Lagrangian systems with symmetry in a way that allows the reduction process to be repeated; that is, it develops a context for Lagrangian reduction by stages. The Lagrangian reduction procedure focuses on the geometry of variational structures and how to reduce them to quotient spaces under group actions. This philosophy is well known for the classical cases, such as Routh reduction for systems with cyclic variables (where the symmetry group is Abelian) and Euler-Poincare reduction (for the case in which the configuration space is a Lie group) as well as Euler-Poincare reduction for semidirect products.
Author | : Hernán Cendra |
Publisher | : |
Total Pages | : 108 |
Release | : 2014-09-11 |
Genre | : Differentiable dynamical systems |
ISBN | : 9781470403157 |
Download Lagrangian Reduction by Stages Book in PDF, ePub and Kindle
Introduction Preliminary constructions The Lagrange-Poincare equations Wong's equations and coordinate formulas The Lie algebra structure on sections of the reduced bundle Reduced tangent bundles Further examples The category $\mathfrak{LP}^*$ and Poisson geometry Bibliography.
Author | : Jerrold E. Marsden |
Publisher | : Springer |
Total Pages | : 524 |
Release | : 2007-06-05 |
Genre | : Mathematics |
ISBN | : 3540724702 |
Download Hamiltonian Reduction by Stages Book in PDF, ePub and Kindle
This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives special emphasis to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. The volume also provides ample background theory on symplectic reduction and cotangent bundle reduction.
Author | : Paul Newton |
Publisher | : Springer Science & Business Media |
Total Pages | : 573 |
Release | : 2006-05-11 |
Genre | : Mathematics |
ISBN | : 0387217916 |
Download Geometry, Mechanics, and Dynamics Book in PDF, ePub and Kindle
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.
Author | : Matthew Perlmutter |
Publisher | : |
Total Pages | : 274 |
Release | : 1999 |
Genre | : |
ISBN | : |
Download Symplectic Reduction by Stages Book in PDF, ePub and Kindle
Author | : Björn Engquist |
Publisher | : Springer |
Total Pages | : 1219 |
Release | : 2017-04-05 |
Genre | : Mathematics |
ISBN | : 364256478X |
Download Mathematics Unlimited - 2001 and Beyond Book in PDF, ePub and Kindle
This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.
Author | : N.P. Landsman |
Publisher | : Birkhäuser |
Total Pages | : 360 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034883641 |
Download Quantization of Singular Symplectic Quotients Book in PDF, ePub and Kindle
This is the first exposition of the quantization theory of singular symplectic (Marsden-Weinstein) quotients and their applications to physics. The reader will acquire an introduction to the various techniques used in this area, as well as an overview of the latest research approaches. These involve classical differential and algebraic geometry, as well as operator algebras and noncommutative geometry. Thus one will be amply prepared to follow future developments in this field.
Author | : Robert A. Meyers |
Publisher | : Springer Science & Business Media |
Total Pages | : 1885 |
Release | : 2011-10-05 |
Genre | : Mathematics |
ISBN | : 1461418054 |
Download Mathematics of Complexity and Dynamical Systems Book in PDF, ePub and Kindle
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Author | : Aleksandr I. Bobenko |
Publisher | : |
Total Pages | : 16 |
Release | : 1999 |
Genre | : |
ISBN | : |
Download Discrete Lagrangian Reduction, Discret Euler-Poincaré Equations and Semidirect Products Book in PDF, ePub and Kindle
Author | : Alexander Mielke |
Publisher | : Springer |
Total Pages | : 145 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540464417 |
Download Hamiltonian and Lagrangian Flows on Center Manifolds Book in PDF, ePub and Kindle
The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds. Nonautonomous problems are considered as well assystems invariant under the action of a Lie group ( including the case of relative equilibria). The theory is applied to elliptic variational problemson cylindrical domains. As a result, all bounded solutions bifurcating from a trivial state can be described by a reduced finite-dimensional variational problem of Lagrangian type. This provides a rigorous justification of rod theory from fully nonlinear three-dimensional elasticity. The book will be of interest to researchers working in classical mechanics, dynamical systems, elliptic variational problems, and continuum mechanics. It begins with the elements of Hamiltonian theory and center manifold reduction in order to make the methods accessible to non-specialists, from graduate student level.