Hamiltonian Reduction by Stages - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hamiltonian Reduction by Stages write by Jerrold E. Marsden. This book was released on 2007-06-05. Hamiltonian Reduction by Stages available 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.
Momentum Maps and Hamiltonian Reduction
Momentum Maps and Hamiltonian Reduction - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Momentum Maps and Hamiltonian Reduction write by Juan-Pablo Ortega. This book was released on 2013-04-17. Momentum Maps and Hamiltonian Reduction available in PDF, EPUB and Kindle. * Winner of the Ferran Sunyer i Balaguer Prize in 2000. * Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds. * Currently in classroom use in Europe. * Can serve as a resource for graduate courses and seminars in Hamiltonian mechanics and symmetry, symplectic and Poisson geometry, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.
Hamiltonian Reduction by Stages
Hamiltonian Reduction by Stages - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hamiltonian Reduction by Stages write by Jerrold E. Marsden. This book was released on 2007. Hamiltonian Reduction by Stages available in PDF, EPUB and Kindle. In this volume readers will find for the first time a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. Special emphasis is given to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. Ample background theory on symplectic reduction and cotangent bundle reduction in particular is provided. Novel features of the book are the inclusion of a systematic treatment of the cotangent bundle case, including the identification of cocycles with magnetic terms, as well as the general theory of singular reduction by stages.
Lagrangian Reduction by Stages
Lagrangian Reduction by Stages - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lagrangian Reduction by Stages write by Hernán Cendra. This book was released on 2001. Lagrangian Reduction by Stages available 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.
Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds
Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds write by Taeyoung Lee. This book was released on 2017-08-14. Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds available in PDF, EPUB and Kindle. This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.
