Global Formulations Of Lagrangian And Hamiltonian Dynamics On Manifolds PDF Download
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Author | : Taeyoung Lee |
Publisher | : Springer |
Total Pages | : 539 |
Release | : 2017-08-14 |
Genre | : Mathematics |
ISBN | : 3319569538 |
Download Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds Book 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.
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.
Author | : G. Giachetta |
Publisher | : World Scientific |
Total Pages | : 472 |
Release | : 1997 |
Genre | : Science |
ISBN | : 9789810215873 |
Download New Lagrangian and Hamiltonian Methods in Field Theory Book in PDF, ePub and Kindle
This book incorporates 3 modern aspects of mathematical physics: the jet methods in differential geometry, Lagrangian formalism on jet manifolds and the multimomentum approach to Hamiltonian formalism. Several contemporary field models are investigated in detail.This is not a book on differential geometry. However, modern concepts of differential geometry such as jet manifolds and connections are used throughout the book. Quadratic Lagrangians and Hamiltonians are studied at the general level including a treatment of Hamiltonian formalism on composite fiber manifolds. The book presents new geometric methods and results in field theory.
Author | : Peter Mann |
Publisher | : Oxford University Press |
Total Pages | : 553 |
Release | : 2018 |
Genre | : Mathematics |
ISBN | : 0198822375 |
Download Lagrangian and Hamiltonian Dynamics Book in PDF, ePub and Kindle
An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Most notable examples include the 'classical wavefunction', Koopman-von Neumann theory, classical density functional theories, the 'vakonomic' variational principle for non-holonomic constraints, the Gibbs-Appell equations, classical path integrals, Nambu brackets and the full framing of mechanics in the language of differential geometry.
Author | : Melvin G. Calkin |
Publisher | : World Scientific |
Total Pages | : 244 |
Release | : 1999 |
Genre | : Science |
ISBN | : 9789810237820 |
Download Lagrangian and Hamiltonian Mechanics Book in PDF, ePub and Kindle
This book contains the exercises from the classical mechanics text Lagrangian and Hamiltonian Mechanics, together with their complete solutions. It is intended primarily for instructors who are using Lagrangian and Hamiltonian Mechanics in their course, but it may also be used, together with that text, by those who are studying mechanics on their own.
Author | : G. Sardanashvily |
Publisher | : World Scientific |
Total Pages | : 168 |
Release | : 1995 |
Genre | : Science |
ISBN | : 9789810220457 |
Download Generalized Hamiltonian Formalism for Field Theory Book in PDF, ePub and Kindle
In the framework of the geometric formulation of field theory, classical fields are represented by sections of fibred manifolds, and their dynamics is phrased in jet manifold terms. The Hamiltonian formalism in fibred manifolds is the multisymplectic generalization of the Hamiltonian formalism in mechanics when canonical momenta correspond to derivatives of fields with respect to all world coordinates, not only to time. This book is devoted to the application of this formalism to fundamental field models including gauge theory, gravitation theory, and spontaneous symmetry breaking. All these models are constraint ones. Their Euler-Lagrange equations are underdetermined and need additional conditions. In the Hamiltonian formalism, these conditions appear automatically as a part of the Hamilton equations, corresponding to different Hamiltonian forms associated with a degenerate Lagrangian density. The general procedure for describing constraint systems with quadratic and affine Lagrangian densities is presented.
Author | : Ovidiu Calin |
Publisher | : Springer Science & Business Media |
Total Pages | : 278 |
Release | : 2006-03-30 |
Genre | : Mathematics |
ISBN | : 0817644210 |
Download Geometric Mechanics on Riemannian Manifolds Book in PDF, ePub and Kindle
* A geometric approach to problems in physics, many of which cannot be solved by any other methods * Text is enriched with good examples and exercises at the end of every chapter * Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics
Author | : Malin Premaratne |
Publisher | : Cambridge University Press |
Total Pages | : 299 |
Release | : 2021-01-07 |
Genre | : Science |
ISBN | : 1108639364 |
Download Theoretical Foundations of Nanoscale Quantum Devices Book in PDF, ePub and Kindle
Nanooptics which describes the interaction of light with matter at the nanoscale, is a topic of great fundamental interest to physicists and engineers and allows the direct observation of quantum mechanical phenomena in action. This self-contained and extensively referenced text describes the underlying theory behind nanodevices operating in the quantum regime for use both in advanced courses and as a reference for researchers in physics, chemistry, electrical engineering, and materials science. Presenting an extensive theoretical toolset for design and analysis of nanodevices, the authors demonstrate the art of developing approximate quantum models of real nanodevices. The rudimentary mathematical knowledge required to master the material is carefully introduced, with detailed derivations and frequent worked examples allowing readers to gain a thorough understanding of the material. More advanced applications are gradually introduced alongside analytical approximations and simplifying assumptions often used to make such problems tractable while representative of the observed features.
Author | : Alexander Mielke |
Publisher | : |
Total Pages | : 152 |
Release | : 2014-09-01 |
Genre | : |
ISBN | : 9783662186572 |
Download Hamiltonian and Lagrangian Flows on Center Manifolds Book in PDF, ePub and Kindle
Author | : Gerardo F. Torres del Castillo |
Publisher | : Springer |
Total Pages | : 366 |
Release | : 2018-09-08 |
Genre | : Mathematics |
ISBN | : 3319952250 |
Download An Introduction to Hamiltonian Mechanics Book in PDF, ePub and Kindle
This textbook examines the Hamiltonian formulation in classical mechanics with the basic mathematical tools of multivariate calculus. It explores topics like variational symmetries, canonoid transformations, and geometrical optics that are usually omitted from an introductory classical mechanics course. For students with only a basic knowledge of mathematics and physics, this book makes those results accessible through worked-out examples and well-chosen exercises. For readers not familiar with Lagrange equations, the first chapters are devoted to the Lagrangian formalism and its applications. Later sections discuss canonical transformations, the Hamilton–Jacobi equation, and the Liouville Theorem on solutions of the Hamilton–Jacobi equation. Graduate and advanced undergraduate students in physics or mathematics who are interested in mechanics and applied math will benefit from this treatment of analytical mechanics. The text assumes the basics of classical mechanics, as well as linear algebra, differential calculus, elementary differential equations and analytic geometry. Designed for self-study, this book includes detailed examples and exercises with complete solutions, although it can also serve as a class text.