Download or read book Hamiltonian Dynamics Theory and Applications written by CIME-EMS Summer School ( and published by Springer Science & Business Media. This book was released on 2005 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hamiltonian Dynamics Theory and Applications written by Giancarlo Benettin and published by Springer. This book was released on 2005-01-14 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hamiltonian Dynamics Theory and Applications written by and published by . This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analytical Dynamics written by Mark D. Ardema and published by Springer Science & Business Media. This book was released on 2006-10-31 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes a traditional approach to the development of the methods of analytical dynamics, using two types of examples throughout: simple illustrations of key results and thorough applications to complex, real-life problems.
Download or read book Hamiltonian Dynamical Systems and Applications written by Walter Craig and published by Springer Science & Business Media. This book was released on 2008-02-17 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hamiltonian Dynamical Systems written by H. S. Dumas and published by . This book was released on 1995-03-10 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hamiltonian Dynamical Systems written by H.S. Dumas and published by Springer Science & Business Media. This book was released on 1995-03-10 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics, some of which were literally created along the way. This volume contains the proceedings of the International Conference on Hamiltonian Dynamical Systems; its contents reflect the wide scope and increasing influence of Hamiltonian methods, with contributions from a whole spectrum of researchers in mathematics and physics from more than half a dozen countries, as well as several researchers in the history of science. With the inclusion of several historical articles, this volume is not only a slice of state-of-the-art methodology in Hamiltonian dynamics, but also a slice of the bigger picture in which that methodology is imbedded.
Download or read book Essentials of Hamiltonian Dynamics written by John H. Lowenstein and published by Cambridge University Press. This book was released on 2012-01-19 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Hamiltonian Dynamics written by Gaetano Vilasi and published by World Scientific. This book was released on 2001 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Hamiltonian Dynamical Systems and the N Body Problem written by Kenneth R. Meyer and published by Springer. This book was released on 2017-05-04 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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)
Download or read book Hamiltonian Chaos and Fractional Dynamics written by George M. Zaslavsky and published by Oxford University Press on Demand. This book was released on 2005 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This books gives a realistic contemporary image of Hamiltonian dynamics, dealing with the basic principles of the Hamiltonian theory of chaos in addition to very recent and unusual applications of nonlinear dynamics and the fractality of dynamics.
Download or read book The Hamiltonian Approach to Dynamic Economics written by David Cass and published by Academic Press. This book was released on 2014-05-10 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Hamiltonian Approach to Dynamic Economics focuses on the application of the Hamiltonian approach to dynamic economics and attempts to provide some unification of the theory of heterogeneous capital. Emphasis is placed on the stability of long-run steady-state equilibrium in models of heterogeneous capital accumulation. Generalizations of the Samuelson-Scheinkman approach are also given. Moreover, conditions are sought on the geometry of the Hamiltonian function (that is, on static technology) that suffice to preserve under (not necessarily small) perturbation the basic properties of the Hamiltonian dynamical system. Comprised of eight essays, this book begins with an introduction to Hamiltonian dynamics in economics, followed by a discussion on optimal steady states of n-sector growth models when utility is discounted. Optimal growth and decentralized or descriptive growth models in both continuous and discrete time are treated as applications of Hamiltonian dynamics. Theproblem of optimal growth with zero discounting is considered, with emphasis on a steepness condition on the Hamiltonian function. The general problem of decentralized growth with instantaneously adjusted expectations about price changes is also analyzed, along with the global asymptotic stability of optimal control systems with applications to the theory of economic growth. This monograph will be of value to mathematicians and economists.
Download or read book Complex Hamiltonian Dynamics written by Tassos Bountis and published by Springer Science & Business Media. This book was released on 2012-04-03 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems. The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) research oriented problems provide many opportunities to deepen the reader’s insights into specific aspects of the subject matter. Addressing a broad audience of graduate students, theoretical physicists and applied mathematicians, this text combines the benefits of a reference work with those of a self-study guide for newcomers to the field.
Download or read book Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds written by Taeyoung Lee and published by Springer. This book was released on 2017-08-14 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lagrangian and Hamiltonian Dynamics written by Peter Mann and published by Oxford University Press. This book was released on 2018 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Dynamics on Differential One Forms written by Troy L. Story and published by iUniverse. This book was released on 2002 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamics on Differential One-Forms proposes a unifying principle for mathematical models of dynamic systems. In "Thermodynamics on One-Forms (chapter I)", the long-standing problem of deriving irreversibility in thermodynamics from reversibility in Hamiltonian mechanics, is solved. Differential geometric analysis shows thermodynamics and Hamiltonian mechanics are both irreversible on representative extended phase spaces. "Dynamics on Differential One-Forms (II)" generalizes (I) to Hamiltonian mechanics, geometric optics, thermodynamics, black holes, electromagnetic fields and string fields. Mathematical models for these systems are revealed as representations of a unifying principle; namely, description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a tangent vector defining system transformations. Relationships between models using exterior calculus and conventional calculus imply a technical definition of dynamic equilibrium. "Global Analysis of Composite Particles (III)" uses differential topology to develop the theory of large vibration-rotation interactions for composite particles. A global classical Hamiltonian and corresponding quantum Hamiltonian operator are derived, then applied to the molecular vibration-rotation problem. "Characteristic Electromagnetic and Yang-Mills Gauge (IV)" uses differential geometry to remove some of the arbitrariness in the gauge, and shows how gauge functions for electromagnetic and Yang-Mills fields follow the same differential equation.
Download or read book Hamiltonian Mechanics of Gauge Systems written by Lev V. Prokhorov and published by Cambridge University Press. This book was released on 2011-09-22 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
