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The Hamiltonian
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Book Synopsis The Hamiltonian Vision, 1789-1800 by : William R. Nester
Download or read book The Hamiltonian Vision, 1789-1800 written by William R. Nester and published by Potomac Books, Inc.. This book was released on 2012 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: The creation of American diplomacy and power as an art
Book Synopsis An Introduction to Hamiltonian Optics by : H. A. Buchdahl
Download or read book An Introduction to Hamiltonian Optics written by H. A. Buchdahl and published by Courier Corporation. This book was released on 1993-01-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Hamilton Phenomenon by : Chloe Northrop
Download or read book The Hamilton Phenomenon written by Chloe Northrop and published by Vernon Press. This book was released on 2022-07-05 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The Hamilton Phenomenon' brings together a diverse group of scholars including university professors and librarians, educators at community colleges, Ph.D. candidates and independent scholars, in an exploration of the celebrated Broadway hit. When Lin-Manuel Miranda’s musical sensation erupted onto Broadway in 2015, scholars were underprepared for the impact the theatrical experience would have. Miranda’s use of rap, hip-hop, jazz, and Broadway show tunes provides the basis for this whirlwind showcase of America’s past through a reinterpretation of eighteenth-century history. Bound together by their shared interest in 'Hamilton: an American Musical', the authors in this volume diverge from a common touchstone to uncover the unique moment presented by this phenomenon. The two parts of this book feature different emerging themes, ranging from the meaning of the musical on stage, to how the musical is impacting pedagogy and teaching in the 21st century. The first part places Hamilton in the history of theatrical performances of the American Revolution, compares it with other musicals, and fleshes out the significance of postcolonial studies within theatrical performances. Esteemed scholars and educators provide the basis for the second part with insights on the efficacy, benefits, and pitfalls of teaching using Hamilton. Although other scholarly works have debated the historical accuracy of Hamilton, 'The Hamilton Phenomenon' benefits from more distance from the release of the musical, as well as the dissemination of the hit through traveling productions and the summer 2020 release on Disney+. Through critically engaging with Hamilton these authors unfold new insights on early American history, pedagogy, costume, race in theatrical performances, and the role of theatre in crafting interest in history.
Book Synopsis Introduction To Classical Mechanics by : John Dirk Walecka
Download or read book Introduction To Classical Mechanics written by John Dirk Walecka and published by World Scientific. This book was released on 2020-02-26 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook aims to provide a clear and concise set of lectures that take one from the introduction and application of Newton's laws up to Hamilton's principle of stationary action and the lagrangian mechanics of continuous systems. An extensive set of accessible problems enhances and extends the coverage.It serves as a prequel to the author's recently published book entitled Introduction to Electricity and Magnetism based on an introductory course taught sometime ago at Stanford with over 400 students enrolled. Both lectures assume a good, concurrent, course in calculus and familiarity with basic concepts in physics; the development is otherwise self-contained.A good introduction to the subject allows one to approach the many more intermediate and advanced texts with better understanding and a deeper sense of appreciation that both students and teachers alike can share.
Book Synopsis Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by : Kenneth R. Meyer
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 384 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)
Book Synopsis Integrable Hamiltonian Systems by : A.V. Bolsinov
Download or read book Integrable Hamiltonian Systems written by A.V. Bolsinov and published by CRC Press. This book was released on 2004-02-25 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,
Book Synopsis Lagrangian and Hamiltonian Dynamics by : Peter Mann
Download or read book Lagrangian and Hamiltonian Dynamics written by Peter Mann and published by Oxford University Press. This book was released on 2018-05-10 with total page 544 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.
Book Synopsis The Hamiltonian Approach to Dynamic Economics by : David Cass
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.
Book Synopsis Metamorphoses of Hamiltonian Systems with Symmetries by : Konstantinos Efstathiou
Download or read book Metamorphoses of Hamiltonian Systems with Symmetries written by Konstantinos Efstathiou and published by Springer. This book was released on 2005-01-28 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.
Book Synopsis Moment Maps, Cobordisms, and Hamiltonian Group Actions by : Victor Guillemin
Download or read book Moment Maps, Cobordisms, and Hamiltonian Group Actions written by Victor Guillemin and published by American Mathematical Soc.. This book was released on 2002 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last 20 years, ``localization'' has been one of the dominant themes in the area of equivariant differential geometry. Typical results are the Duistermaat-Heckman theory, the Berline-Vergne-Atiyah-Bott localization theorem in equivariant de Rham theory, and the ``quantization commutes with reduction'' theorem and its various corollaries. To formulate the idea that these theorems are all consequences of a single result involving equivariant cobordisms, the authors have developed a cobordism theory that allows the objects to be non-compact manifolds. A key ingredient in this non-compact cobordism is an equivariant-geometrical object which they call an ``abstract moment map''. This is a natural and important generalization of the notion of a moment map occurring in the theory of Hamiltonian dynamics. The book contains a number of appendices that include introductions to proper group-actions on manifolds, equivariant cohomology, Spin${^\mathrm{c}}$-structures, and stable complex structures. It is geared toward graduate students and research mathematicians interested in differential geometry. It is also suitable for topologists, Lie theorists, combinatorists, and theoretical physicists. Prerequisite is some expertise in calculus on manifolds and basic graduate-level differential geometry.
Book Synopsis On the Splitting of Invariant Manifolds in Multidimensional Near-Integrable Hamiltonian Systems by : Pierre Lochak
Download or read book On the Splitting of Invariant Manifolds in Multidimensional Near-Integrable Hamiltonian Systems written by Pierre Lochak and published by American Mathematical Soc.. This book was released on 2003 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the problem of the splitting of invariant manifolds in multidimensional Hamiltonian systems, stressing the canonical features of the problem. This book offers introduction of a canonically invariant scheme for the computation of the splitting matrix.
Book Synopsis An Introduction to Hamiltonian Mechanics by : Gerardo F. Torres del Castillo
Download or read book An Introduction to Hamiltonian Mechanics written by Gerardo F. Torres del Castillo and published by Springer. This book was released on 2018-09-08 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Hamiltonian Partial Differential Equations and Applications by : Philippe Guyenne
Download or read book Hamiltonian Partial Differential Equations and Applications written by Philippe Guyenne and published by Springer. This book was released on 2015-09-11 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.
Book Synopsis Essentials of Hamiltonian Dynamics by : John H. Lowenstein
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 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.
Book Synopsis Integrable Hamiltonian Systems on Complex Lie Groups by : Velimir Jurdjevic
Download or read book Integrable Hamiltonian Systems on Complex Lie Groups written by Velimir Jurdjevic and published by American Mathematical Soc.. This book was released on 2005 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies the elastic problems on simply connected manifolds $M_n$ whose orthonormal frame bundle is a Lie group $G$. This title synthesizes ideas from optimal control theory, adapted to variational problems on the principal bundles of Riemannian spaces, and the symplectic geometry of the Lie algebra $\mathfrak{g}, $ of $G$
Book Synopsis Hamiltonian Dynamical Systems by : R.S MacKay
Download or read book Hamiltonian Dynamical Systems written by R.S MacKay and published by CRC Press. This book was released on 1987-01-01 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Hamiltonian Field Theory in the Radiating Regime by : Piotr T. Chrusciel
Download or read book Hamiltonian Field Theory in the Radiating Regime written by Piotr T. Chrusciel and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this monograph is to show that, in the radiation regime, there exists a Hamiltonian description of the dynamics of a massless scalar field, as well as of the dynamics of the gravitational field. The authors construct such a framework extending the previous work of Kijowski and Tulczyjew. They start by reviewing some elementary facts concerning Hamiltonian dynamical systems and then describe the geometric Hamiltonian framework, adequate for both the usual asymptotically-flat-at-spatial-infinity regime and for the radiation regime. The text then gives a detailed description of the application of the new formalism to the case of the massless scalar field. Finally, the formalism is applied to the case of Einstein gravity. The Hamiltonian role of the Trautman--Bondi mass is exhibited. A Hamiltonian definition of angular momentum at null infinity is derived and analysed.
