Essentials of Hamiltonian Dynamics PDF Download

Author: John H. Lowenstein
Publisher: Cambridge University Press
ISBN: 1107005205
Category : Mathematics
Languages : en
Pages : 203

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Book Description
Concise and pedagogical textbook that covers all the topics necessary for a graduate-level course in dynamics based on Hamiltonian methods.

Author: John H. Lowenstein
Publisher: Cambridge University Press
ISBN: 1139504738
Category : Science
Languages : en
Pages : 203

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Book Description
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.

Author: Cram101 Textbook Reviews
Publisher: Cram101
ISBN: 9781478467335
Category :
Languages : en
Pages : 74

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Book Description
Never HIGHLIGHT a Book Again Includes all testable terms, concepts, persons, places, and events. Cram101 Just the FACTS101 studyguides gives all of the outlines, highlights, and quizzes for your textbook with optional online comprehensive practice tests. Only Cram101 is Textbook Specific. Accompanies: 9780872893795. This item is printed on demand.

Author: Cram101 Textbook Reviews
Publisher: Cram101
ISBN: 9781478443209
Category :
Languages : en
Pages : 136

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Book Description
Never HIGHLIGHT a Book Again! Virtually all of the testable terms, concepts, persons, places, and events from the textbook are included. Cram101 Just the FACTS101 studyguides give all of the outlines, highlights, notes, and quizzes for your textbook with optional online comprehensive practice tests. Only Cram101 is Textbook Specific. Accompanys: 9781111833862 .

Author: Gaetano Vilasi
Publisher: World Scientific
ISBN: 9789812386311
Category : Mathematics
Languages : en
Pages : 460

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Book Description
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 Coordinates; Hamiltonian Systems; Transformation Theory; The Integration Methods; Basic Ideas of Differential Geometry: Manifolds and Tangent Spaces; Differential Forms; Integration Theory; Lie Groups and Lie Algebras; Geometry and Physics: Symplectic Manifolds and Hamiltonian Systems; The Orbits Method; Classical Electrodynamics; Integrable Field Theories: KdV Equation; General Structures; Meaning and Existence of Recursion Operators; Miscellanea; Integrability of Fermionic Dynamics. Readership: Physicists and mathematicians.

Author: Tassos Bountis
Publisher: Springer Science & Business Media
ISBN: 3642273041
Category : Language Arts & Disciplines
Languages : en
Pages : 277

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Book Description
This book explores modern developments in Hamiltonian dynamical systems, focusing on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. Includes end-of-chapter exercises and challenging problems.

Author: Gerardo F. Torres del Castillo
Publisher: Birkhäuser
ISBN: 9783319952246
Category : Mathematics
Languages : en
Pages : 366

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Book Description
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.

Author: Taeyoung Lee
Publisher: Springer
ISBN: 3319569538
Category : Mathematics
Languages : en
Pages : 561

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Book Description
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: Giancarlo Benettin
Publisher: Springer
ISBN: 3540315411
Category : Mathematics
Languages : en
Pages : 187

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Book Description
This volume compiles three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim is to describe the state of the art for some interesting problems, such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants, and the phenomena related to stability over exponentially long times of Nekhoroshev's theory. The books may serve as an excellent basis for young researchers, who will find here a complete and accurate exposition of recent original results and many hints for further investigation.

Author: Benedict Leimkuhler
Publisher: Cambridge University Press
ISBN: 9780521772907
Category : Mathematics
Languages : en
Pages : 464

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Book Description
Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.