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| 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 | : William R. Nester |
| Publisher | : Potomac Books, Inc. |
| Total Pages | : 291 |
| Release | : 2012 |
| Genre | : Biography & Autobiography |
| ISBN | : 1597978833 |
Download The Hamiltonian Vision, 1789-1800 Book in PDF, ePub and Kindle
The creation of American diplomacy and power as an art
| Author | : John Dirk Walecka |
| Publisher | : World Scientific |
| Total Pages | : 184 |
| Release | : 2020-02-26 |
| Genre | : Science |
| ISBN | : 9811217459 |
Download Introduction To Classical Mechanics Book in PDF, ePub and Kindle
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.
| Author | : Chloe Northrop |
| Publisher | : Vernon Press |
| Total Pages | : 252 |
| Release | : 2022-07-05 |
| Genre | : History |
| ISBN | : 1648894224 |
Download The Hamilton Phenomenon Book in PDF, ePub and Kindle
'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.
| 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 | : Peter Mann |
| Publisher | : Oxford University Press |
| Total Pages | : 544 |
| Release | : 2018-05-10 |
| Genre | : Science |
| ISBN | : 0192555413 |
Download Lagrangian and Hamiltonian Dynamics Book in PDF, ePub and Kindle
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.
| 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 | : Konstantinos Efstathiou |
| Publisher | : Springer |
| Total Pages | : 149 |
| Release | : 2005-01-28 |
| Genre | : Science |
| ISBN | : 3540315500 |
Download Metamorphoses of Hamiltonian Systems with Symmetries Book in PDF, ePub and Kindle
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.
| Author | : Antonio Giorgilli |
| Publisher | : Cambridge University Press |
| Total Pages | : 474 |
| Release | : 2022-05-05 |
| Genre | : Science |
| ISBN | : 100917486X |
Download Notes on Hamiltonian Dynamical Systems Notes on Hamiltonian Dynamical Systems Book in PDF, ePub and Kindle
Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov–Arnold–Moser theorem, Nekhoroshev's theorem and superexponential stability. Its analytic approach allows students to learn about perturbation methods leading to advanced results. Key topics covered include Liouville's theorem, the proof of Poincaré's non-integrability theorem and the nonlinear dynamics in the neighbourhood of equilibria. The theorem of Kolmogorov on persistence of invariant tori and the theory of exponential stability of Nekhoroshev are proved via constructive algorithms based on the Lie series method. A final chapter is devoted to the discovery of chaos by Poincaré and its relations with integrability, also including recent results on superexponential stability. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students.
