Essentials of Hamiltonian Dynamics

Author: John H. Lowenstein
Publisher: Cambridge University Press
ISBN: 1107005205
Format: PDF, ePub, Docs
Download Now
Concise and pedagogical textbook that covers all the topics necessary for a graduate-level course in dynamics based on Hamiltonian methods.

Essentials of Hamiltonian Dynamics

Author: John H. Lowenstein
Publisher: Cambridge University Press
ISBN: 1107005205
Format: PDF, ePub, Mobi
Download Now
Concise and pedagogical textbook that covers all the topics necessary for a graduate-level course in dynamics based on Hamiltonian methods.

Essentials of Hamiltonian Dynamics

Author: CTI Reviews
Publisher: Cram101 Textbook Reviews
ISBN: 1478449969
Format: PDF, Kindle
Download Now
Facts101 is your complete guide to Essentials of Hamiltonian Dynamics. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Hamiltonian Dynamics

Author: Gaetano Vilasi
Publisher: World Scientific
ISBN: 9814496731
Format: PDF, Mobi
Download Now
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. Contents:Analytical Mechanics:The Lagrangian CoordinatesHamiltonian SystemsTransformation TheoryThe Integration MethodsBasic Ideas of Differential Geometry:Manifolds and Tangent SpacesDifferential FormsIntegration TheoryLie Groups and Lie AlgebrasGeometry and Physics:Symplectic Manifolds and Hamiltonian SystemsThe Orbits MethodClassical ElectrodynamicsIntegrable Field Theories:KdV EquationGeneral StructuresMeaning and Existence of Recursion OperatorsMiscellaneaIntegrability of Fermionic Dynamics Readership: Physicists and mathematicians. keywords:Lagrangian;Hamiltonian;Manifold;Bundle;Tensors;Group;Algebra;Curvature;Symplectic;Integrability;Electrodynamics;Soliton “The book is clearly written with concise historical notes and a quite complete set of suggested readings and references … it can be very useful both as a textbook in analytical mechanics and as a first introduction to Hamiltonian dynamics in infinite dimensions.” Mathematical Reviews

Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds

Author: Taeyoung Lee
Publisher: Springer
ISBN: 3319569538
Format: PDF, Kindle
Download Now
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.

Classical Mechanics

Author: Walter Greiner
Publisher: Springer Science & Business Media
ISBN: 9783642034343
Format: PDF
Download Now
The series of texts on Classical Theoretical Physics is based on the highly successful courses given by Walter Greiner. The volumes provide a complete survey of classical theoretical physics and an enormous number of worked out examples and problems.

Symplectic Invariants and Hamiltonian Dynamics

Author: Helmut Hofer
Publisher: Springer Science & Business Media
ISBN: 9783034801041
Format: PDF, ePub, Mobi
Download Now
The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: symplectic topology. Surprising rigidity phenomena demonstrate that the nature of symplectic mappings is very different from that of volume preserving mappings. This raises new questions, many of them still unanswered. On the other hand, analysis of an old variational principle in classical mechanics has established global periodic phenomena in Hamiltonian systems. As it turns out, these seemingly different phenomena are mysteriously related. One of the links is a class of symplectic invariants, called symplectic capacities. These invariants are the main theme of this book, which includes such topics as basic symplectic geometry, symplectic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a bi-invariant metric on the symplectic diffeomorphism group and its geometry, symplectic fixed point theory, the Arnold conjectures and first order elliptic systems, and finally a survey on Floer homology and symplectic homology. The exposition is self-contained and addressed to researchers and students from the graduate level onwards.

An Introduction to Lagrangian Mechanics

Author: Alain J Brizard
Publisher: World Scientific Publishing Company
ISBN: 9814623644
Format: PDF, Mobi
Download Now
An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d'Alembert that preceded Hamilton's formulation of the Principle of Least Action, from which the Euler–Lagrange equations of motion are derived. Other additional topics not traditionally presented in undergraduate textbooks include the treatment of constraint forces in Lagrangian Mechanics; Routh's procedure for Lagrangian systems with symmetries; the art of numerical analysis for physical systems; variational formulations for several continuous Lagrangian systems; an introduction to elliptic functions with applications in Classical Mechanics; and Noncanonical Hamiltonian Mechanics and perturbation theory. The Second Edition includes a larger selection of examples and problems (with hints) in each chapter and continues the strong emphasis of the First Edition on the development and application of mathematical methods (mostly calculus) to the solution of problems in Classical Mechanics. New material has been added to most chapters. For example, a new derivation of the Noether theorem for discrete Lagrangian systems is given and a modified Rutherford scattering problem is solved exactly to show that the total scattering cross section associated with a confined potential (i.e., which vanishes beyond a certain radius) yields the hard-sphere result. The Frenet-Serret formulas for the Coriolis-corrected projectile motion are presented, where the Frenet-Serret torsion is shown to be directly related to the Coriolis deflection, and a new treatment of the sleeping-top problem is given.

Lagrangian and Hamiltonian Mechanics

Author: M G Calkin
Publisher: World Scientific Publishing Company
ISBN: 9813105410
Format: PDF, Mobi
Download Now
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.