Lagrangian Reduction By Stages
DOWNLOAD
Download Lagrangian Reduction By Stages PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Lagrangian Reduction By Stages book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Lagrangian Reduction By Stages
DOWNLOAD
Author : Hernán Cendra
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Lagrangian Reduction By Stages written by Hernán Cendra and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
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.
Lagrangian Reduction By Stages
DOWNLOAD
Author : Hernán Cendra
language : en
Publisher:
Release Date : 2014-09-11
Lagrangian Reduction By Stages written by Hernán Cendra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Differentiable dynamical systems categories.
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.
Lagrangian Reduction By Stages
DOWNLOAD
Author : Hernn Cendra
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-06-15
Lagrangian Reduction By Stages written by Hernn Cendra and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-15 with Mathematics categories.
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. The context established for this theory is a Lagrangian analogue of the bundle picture on the Hamiltonian side. In this picture, we develop a category that includes, as a special case, the realization of the quotient of a tangent bundle as the Whitney sum of the tangent of the quotient bundle with the associated adjoint bundle. The elements of this new category, called the Lagrange-Poincare category, have enough geometric structure so that the category is stable under the procedure of Lagrangian reduction. Thus, reduction may be repeated, giving the desired context for reduction by stages. Our category may be viewed as a Lagrangian analog of the category of Poisson manifolds in Hamiltonian theory. We also give an intrinsic and geometric way of writing the reduced equations, called the Lagrange-Poincare equations, using covariant derivatives and connections. In addition, the context includes the interpretation of cocycles as curvatures of connections and is general enough to encompass interesting situations involving both semidirect products and central extensions. Examples are given to illustrate the general theory. In classical Routh reduction one usually sets the conserved quantities conjugate to the cyclic variables equal to a constant. In our development, we do not require the imposition of this constraint. For the general theory along these lines, we refer to the complementary work of [2000], which studies the Lagrange-Routh equations.
Hamiltonian Reduction By Stages
DOWNLOAD
Author : Jerrold E. Marsden
language : en
Publisher: Springer
Release Date : 2007-06-05
Hamiltonian Reduction By Stages written by Jerrold E. Marsden and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-05 with Mathematics categories.
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.
Lagrangian Reduction Of Nonholonomic Systems On Semidirect Products
DOWNLOAD
Author : Meihua Tai
language : en
Publisher:
Release Date : 2001
Lagrangian Reduction Of Nonholonomic Systems On Semidirect Products written by Meihua Tai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
Symplectic Reduction By Stages
DOWNLOAD
Author : Matthew Perlmutter
language : en
Publisher:
Release Date : 1999
Symplectic Reduction By Stages written by Matthew Perlmutter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Geometry Mechanics And Dynamics
DOWNLOAD
Author : Paul Newton
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-11
Geometry Mechanics And Dynamics written by Paul Newton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-11 with Mathematics categories.
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.
Discrete Lagrangian Reduction Discret Euler Poincar Equations And Semidirect Products
DOWNLOAD
Author : Aleksandr I. Bobenko
language : en
Publisher:
Release Date : 1999
Discrete Lagrangian Reduction Discret Euler Poincar Equations And Semidirect Products written by Aleksandr I. Bobenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
Mathematics Unlimited 2001 And Beyond
DOWNLOAD
Author : Björn Engquist
language : en
Publisher: Springer
Release Date : 2017-04-05
Mathematics Unlimited 2001 And Beyond written by Björn Engquist and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-05 with Mathematics categories.
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.
Discrete Lagrangian Reduction Discrete Euler Poincar Equations And Semidirect Products
DOWNLOAD
Author : Alexander I. Bobenko
language : en
Publisher:
Release Date : 1999
Discrete Lagrangian Reduction Discrete Euler Poincar Equations And Semidirect Products written by Alexander I. Bobenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.