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| Author | : Gaetano Vilasi |
| Publisher | : World Scientific |
| Total Pages | : 457 |
| Release | : 2001 |
| Genre | : Science |
| ISBN | : 9810233086 |
Download Hamiltonian Dynamics Book 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.
| Author | : Kenneth R. Meyer |
| Publisher | : Springer |
| Total Pages | : 384 |
| Release | : 2017-05-04 |
| Genre | : Mathematics |
| ISBN | : 3319536915 |
Download Introduction to Hamiltonian Dynamical Systems and the N-Body Problem Book 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)
| Author | : H. A. Buchdahl |
| Publisher | : Courier Corporation |
| Total Pages | : 392 |
| Release | : 1993-01-01 |
| Genre | : Science |
| ISBN | : 9780486675978 |
Download An Introduction to Hamiltonian Optics Book in PDF, ePub and Kindle
Accessible study provides detailed account of the Hamiltonian treatment of aberration theory in geometrical optics. Many classes of optical systems defined in terms of their symmetries. Detailed solutions. 1970 edition.
| Author | : John H. Lowenstein |
| Publisher | : Cambridge University Press |
| Total Pages | : 203 |
| Release | : 2012-01-19 |
| Genre | : Science |
| ISBN | : 1139504738 |
Download Essentials of Hamiltonian Dynamics Book 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.
| Author | : Birgit Jacob |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 221 |
| Release | : 2012-06-13 |
| Genre | : Science |
| ISBN | : 3034803990 |
Download Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces Book in PDF, ePub and Kindle
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An abstract functional analytical approach is combined with the physical approach to Hamiltonian systems. This combined approach leads to easily verifiable conditions for well-posedness and stability. The book is accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Moreover, the theory is illustrated by many worked-out examples.
| 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 | : |
| Publisher | : |
| Total Pages | : 844 |
| Release | : 1917 |
| Genre | : United States |
| ISBN | : |
Download The Hamiltonian Book in PDF, ePub and Kindle
| Author | : R.S MacKay |
| Publisher | : CRC Press |
| Total Pages | : 797 |
| Release | : 2020-08-17 |
| Genre | : Mathematics |
| ISBN | : 100011208X |
Download Hamiltonian Dynamical Systems Book in PDF, ePub and Kindle
Classical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which means that potential readers may be somewhat discouraged by the effort required to obtain them. Addressing this situation, Hamiltonian Dynamical Systems includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting order and chaos. It begins with an introductory survey of the subjects to help readers appreciate the underlying themes that unite an apparently diverse collection of articles. The book concludes with a selection of papers on applications, including in celestial mechanics, plasma physics, chemistry, accelerator physics, fluid mechanics, and solid state mechanics, and contains an extensive bibliography. The book provides a worthy introduction to the subject for anyone with an undergraduate background in physics or mathematics, and an indispensable reference work for researchers and graduate students interested in any aspect of classical mechanics.
| Author | : Walter Craig |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 450 |
| Release | : 2008-02-17 |
| Genre | : Mathematics |
| ISBN | : 1402069642 |
Download Hamiltonian Dynamical Systems and Applications Book in PDF, ePub and Kindle
This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.
| Author | : Lev V. Prokhorov |
| Publisher | : Cambridge University Press |
| Total Pages | : 485 |
| Release | : 2011-09-22 |
| Genre | : Science |
| ISBN | : 1139500902 |
Download Hamiltonian Mechanics of Gauge Systems Book in PDF, ePub and Kindle
The principles of gauge symmetry and quantization are fundamental to modern understanding of the laws of electromagnetism, weak and strong subatomic forces and the theory of general relativity. Ideal for graduate students and researchers in theoretical and mathematical physics, this unique book provides a systematic introduction to Hamiltonian mechanics of systems with gauge symmetry. The book reveals how gauge symmetry may lead to a non-trivial geometry of the physical phase space and studies its effect on quantum dynamics by path integral methods. It also covers aspects of Hamiltonian path integral formalism in detail, along with a number of related topics such as the theory of canonical transformations on phase space supermanifolds, non-commutativity of canonical quantization and elimination of non-physical variables. The discussion is accompanied by numerous detailed examples of dynamical models with gauge symmetries, clearly illustrating the key concepts.
