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.
Essentials of Hamiltonian Dynamics
Essentials of 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 Essentials of Hamiltonian Dynamics write by John H. Lowenstein. This book was released on 2012-01-19. Essentials of Hamiltonian Dynamics available in PDF, EPUB and Kindle. Classical dynamics is one of the cornerstones of advanced education in physics and applied mathematics, with applications across engineering, chemistry and biology. In this book, the author uses a concise and pedagogical style to cover all the topics necessary for a graduate-level course in dynamics based on Hamiltonian methods. Readers are introduced to the impressive advances in the field during the second half of the twentieth century, including KAM theory and deterministic chaos. Essential to these developments are some exciting ideas from modern mathematics, which are introduced carefully and selectively. Core concepts and techniques are discussed, together with numerous concrete examples to illustrate key principles. A special feature of the book is the use of computer software to investigate complex dynamical systems, both analytically and numerically. This text is ideal for graduate students and advanced undergraduates who are already familiar with the Newtonian and Lagrangian treatments of classical mechanics. The book is well suited to a one-semester course, but is easily adapted to a more concentrated format of one-quarter or a trimester. A solutions manual and introduction to Mathematica® are available online at www.cambridge.org/Lowenstein.
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 2001-03-09. 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.
Symplectic Invariants and Hamiltonian Dynamics
Symplectic Invariants and 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 Symplectic Invariants and Hamiltonian Dynamics write by Helmut Hofer. This book was released on 2012-12-06. Symplectic Invariants and Hamiltonian Dynamics available in PDF, EPUB and Kindle. Analysis of an old variational principal in classical mechanics has established global periodic phenomena in Hamiltonian systems. One of the links is a class of sympletic invariants, called sympletic capacities, and these invariants are the main theme of this book. Topics covered include basic sympletic geometry, sympletic capacities and rigidity, sympletic fixed point theory, and a survey on Floer homology and sympletic homology.
Introduction to Hamiltonian Dynamical Systems and the N-Body Problem
Introduction to Hamiltonian Dynamical Systems and the N-Body Problem - 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 Introduction to Hamiltonian Dynamical Systems and the N-Body Problem write by Kenneth R. Meyer. This book was released on 2017-05-04. Introduction to Hamiltonian Dynamical Systems and the N-Body Problem available in PDF, EPUB and Kindle. This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. ... It is a well-organized and accessible introduction to the subject ... . This is an attractive book ... ." (William J. Satzer, The Mathematical Association of America, March, 2009) “The second edition of this text infuses new mathematical substance and relevance into an already modern classic ... and is sure to excite future generations of readers. ... This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. ... it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.” (Marian Gidea, Mathematical Reviews, Issue 2010 d)
