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.
Hamiltonian and Lagrangian Dynamics
Hamiltonian and Lagrangian Dynamics - 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 and Lagrangian Dynamics write by James Curry. This book was released on 2011-08. Hamiltonian and Lagrangian Dynamics available in PDF, EPUB and Kindle. This is a text on Hamiltonian and Lagrangian Mechanics designed for use by students who have just finished the Calculus sequence. However, there is enough advanced material that it could also serve for a first year graduate course in Classical Mechanics. It might be used as a principal text or as a reference, or as a lifeboat, in either case. The book distinguishes itself by providing an unusually geometric approach. Here, we introduce Hamiltonian Dynamics first, as it is more intuitive, since the Hamitonian is the "energy" of the system. Then we develop Lagrangian Dynamics. I have devoted early chapters modern mathematics, meaning Group Theory, Linear Algebra, Functional Analysis, and some Differential Geometry. We then exploit this material to present Dynamical Systems more clearly. This book may also be useful to mathematics students who might want a gentle and painless introduction to modern mathematics, and a chance to see what it can do.
Hamiltonian and Lagrangian Flows on Center Manifolds
Hamiltonian and Lagrangian Flows on Center 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 Hamiltonian and Lagrangian Flows on Center Manifolds write by Alexander Mielke. This book was released on 2006-11-14. Hamiltonian and Lagrangian Flows on Center Manifolds available 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.
Solved Problems in Lagrangian and Hamiltonian Mechanics
Solved Problems in Lagrangian and Hamiltonian Mechanics - 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 Solved Problems in Lagrangian and Hamiltonian Mechanics write by Claude Gignoux. This book was released on 2009-07-17. Solved Problems in Lagrangian and Hamiltonian Mechanics available in PDF, EPUB and Kindle. The aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.
Hamiltonian Dynamics
Hamiltonian Dynamics - 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 Dynamics write by Gaetano Vilasi. This book was released on 2001. Hamiltonian Dynamics available in PDF, EPUB and Kindle. This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems.As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity.As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations.
