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Author : Patrick Hamill
Publisher : Cambridge University Press
Page : 185 pages
File Size : 44,6 Mb
Release : 2014
Category : Mathematics
ISBN : 9781107042889
A concise treatment of variational techniques, focussing on Lagrangian and Hamiltonian systems, ideal for physics, engineering and mathematics students.
Author : Melvin G Calkin
Publisher : World Scientific Publishing Company
Page : 240 pages
File Size : 46,8 Mb
Release : 1999-03-12
Category : Science
ISBN : 9789813105416
This book contains the exercises from the classical mechanics text Lagrangian and Hamiltonian Mechanics, together with their complete solutions. It is intended primarily for instructors who are using Lagrangian and Hamiltonian Mechanics in their course, but it may also be used, together with that text, by those who are studying mechanics on their own.
Author : Don S. Lemons
Publisher : Cambridge University Press
Page : 195 pages
File Size : 45,6 Mb
Release : 2013-08-29
Category : Science
ISBN : 9781107470040
Striving to explore the subject in as simple a manner as possible, this book helps readers understand the elusive concept of entropy. Innovative aspects of the book include the construction of statistical entropy from desired properties, the derivation of the entropy of classical systems from purely classical assumptions, and a statistical thermodynamics approach to the ideal Fermi and ideal Bose gases. Derivations are worked through step-by-step and important applications are highlighted in over 20 worked examples. Around 50 end-of-chapter exercises test readers' understanding. The book also features a glossary giving definitions for all essential terms, a time line showing important developments, and list of books for further study. It is an ideal supplement to undergraduate courses in physics, engineering, chemistry and mathematics.
Author : Sanjoy Mahajan
Publisher : Cambridge University Press
Page : 215 pages
File Size : 49,8 Mb
Release : 2020-06-18
Category : Science
ISBN : 9781108471145
Master Newton's laws of motion, the basis of modern science and engineering, with this intuitive and accessible text.
Author : Patrick Hamill
Publisher : Cambridge University Press
Page : 617 pages
File Size : 51,5 Mb
Release : 2022-04-21
Category : Science
ISBN : 9781009098472
A comprehensive but accessible advanced undergraduate treatment of classical mechanics, adaptable to a one or two-semester course.
Author : Taeyoung Lee,Melvin Leok,N. Harris McClamroch
Publisher : Springer
Page : 539 pages
File Size : 44,9 Mb
Release : 2017-08-14
Category : Mathematics
ISBN : 9783319569536
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 : John L. Bohn
Publisher : Cambridge University Press
Page : 219 pages
File Size : 48,7 Mb
Release : 2018-08-30
Category : Science
ISBN : 9781107145764
An accessible guide to analytical mechanics, using intuitive examples to illustrate the underlying mathematics, helping students formulate, solve and interpret problems in mechanics.
Author : Peter Mann
Publisher : Oxford University Press
Page : 553 pages
File Size : 54,9 Mb
Release : 2018
Category : Mathematics
ISBN : 9780198822370
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 : Leonard Susskind,George Hrabovsky
Publisher : Basic Books
Page : 165 pages
File Size : 45,6 Mb
Release : 2014-04-22
Category : Education
ISBN : 9780465038923
A master teacher presents the ultimate introduction to classical mechanics for people who are serious about learning physics "Beautifully clear explanations of famously 'difficult' things," -- Wall Street Journal If you ever regretted not taking physics in college -- or simply want to know how to think like a physicist -- this is the book for you. In this bestselling introduction to classical mechanics, physicist Leonard Susskind and hacker-scientist George Hrabovsky offer a first course in physics and associated math for the ardent amateur. Challenging, lucid, and concise, The Theoretical Minimum provides a tool kit for amateur scientists to learn physics at their own pace.
Author : Claude Gignoux,Bernard Silvestre-Brac
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 41,7 Mb
Release : 2009-07-14
Category : Science
ISBN : 9789048123933
The aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.
Author : Don S. Lemons
Publisher : Princeton University Press
Page : 132 pages
File Size : 45,7 Mb
Release : 2020-06-30
Category : Science
ISBN : 9780691214825
What does the path taken by a ray of light share with the trajectory of a thrown baseball and the curve of a wheat stalk bending in the breeze? Each is the subject of a different study yet all are optimal shapes; light rays minimize travel time while a thrown baseball minimizes action. All natural curves and shapes, and many artificial ones, manifest such "perfect form" because physical principles can be expressed as a statement requiring some important physical quantity to be mathematically maximum, minimum, or stationary. Perfect Form introduces the basic "variational" principles of classical physics (least time, least potential energy, least action, and Hamilton's principle), develops the mathematical language most suited to their application (the calculus of variations), and presents applications from the physics usually encountered in introductory course sequences. The text gradually unfolds the physics and mathematics. While other treatments postulate Hamilton's principle and deduce all results from it, Perfect Form begins with the most plausible and restricted variational principles and develops more powerful ones through generalization. One selection of text and problems even constitutes a non-calculus of variations introduction to variational methods, while the mathematics more generally employed extends only to solving simple ordinary differential equations. Perfect Form is designed to supplement existing classical mechanics texts and to present variational principles and methods to students who approach the subject for the first time.
Author : Daniel Fleisch,Laura Kinnaman
Publisher : Cambridge University Press
Page : 231 pages
File Size : 48,7 Mb
Release : 2015-04-09
Category : Science
ISBN : 9781107054868
Written to complement course textbooks, this book focuses on the topics that undergraduates in physics and engineering find most difficult.
Author : Lev V. Prokhorov,Sergei V. Shabanov
Publisher : Cambridge University Press
Page : 485 pages
File Size : 44,9 Mb
Release : 2011-09-22
Category : Science
ISBN : 9781139500906
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.
Author : Mark Levi
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 40,5 Mb
Release : 2014-03-07
Category : Mathematics
ISBN : 9780821891384
This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.
Author : Dwight E. Neuenschwander
Publisher : JHU Press
Page : 338 pages
File Size : 50,5 Mb
Release : 2017-04-01
Category : Science
ISBN : 9781421422688
One of the most important—and beautiful—mathematical solutions ever devised, Noether’s theorem touches on every aspect of physics. "In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began."—Albert Einstein The year was 1915, and the young mathematician Emmy Noether had just settled into Göttingen University when Albert Einstein visited to lecture on his nearly finished general theory of relativity. Two leading mathematicians of the day, David Hilbert and Felix Klein, dug into the new theory with gusto, but had difficulty reconciling it with what was known about the conservation of energy. Knowing of her expertise in invariance theory, they requested Noether’s help. To solve the problem, she developed a novel theorem, applicable across all of physics, which relates conservation laws to continuous symmetries—one of the most important pieces of mathematical reasoning ever developed. Noether’s “first” and “second” theorem was published in 1918. The first theorem relates symmetries under global spacetime transformations to the conservation of energy and momentum, and symmetry under global gauge transformations to charge conservation. In continuum mechanics and field theories, these conservation laws are expressed as equations of continuity. The second theorem, an extension of the first, allows transformations with local gauge invariance, and the equations of continuity acquire the covariant derivative characteristic of coupled matter-field systems. General relativity, it turns out, exhibits local gauge invariance. Noether’s theorem also laid the foundation for later generations to apply local gauge invariance to theories of elementary particle interactions. In Dwight E. Neuenschwander’s new edition of Emmy Noether’s Wonderful Theorem, readers will encounter an updated explanation of Noether’s “first” theorem. The discussion of local gauge invariance has been expanded into a detailed presentation of the motivation, proof, and applications of the “second” theorem, including Noether’s resolution of concerns about general relativity. Other refinements in the new edition include an enlarged biography of Emmy Noether’s life and work, parallels drawn between the present approach and Noether’s original 1918 paper, and a summary of the logic behind Noether’s theorem.
