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Richard Feynman s never previously published doctoral thesis formed the heart of much of his brilliant and profound work in theoretical physics. Entitled The Principle of Least Action in Quantum Mechanics, its original motive was to quantize the classical action-at-a-distance electrodynamics. Because that theory adopted an overall space time viewpoint, the classical Hamiltonian approach used in the conventional formulations of quantum theory could not be used, so Feynman turned to the Lagrangian function and the principle of least action as his points of departure.

The result was the path integral approach, which satisfied -- and transcended -- its original motivation, and has enjoyed great success in renormalized quantum field theory, including the derivation of the ubiquitous Feynman diagrams for elementary particles. Path integrals have many other applications, including atomic, molecular, and nuclear scattering, statistical mechanics, quantum liquids and solids, Brownian motion, and noise theory. It also sheds new light on fundamental issues like the interpretation of quantum theory because of its new overall space time viewpoint.

The present volume includes Feynman s Princeton thesis, the related review article Space Time Approach to Non-Relativistic Quantum Mechanics [Reviews of Modern Physics 20 (1948), 367 387], Paul Dirac s seminal paper The Lagrangian in Quantum Mechanics [Physikalische Zeitschrift der Sowjetunion, Band 3, Heft 1 (1933)], and an introduction by Laurie M Brown.

Contents: Least Action in Classical Mechanics: The Concept of Functional; The Principle of Least Action; Conservation of Energy. Constants of the Motion; Particles Interacting Through an Intermediate Oscillator; Least Action in Quantum Mechanics: The Lagrangian in Quantum Mechanics; The Calculation of Matrix Elements in the Language of a Lagrangian; The Equations of Motion in Lagrangian Form; Translation to the Ordinary Notation of Quantum Mechanics; The Generalization to Any Action Function; Conservation of Energy. Constants of the Motion; The Role of the Wave Function; Transition Probabilities; Expectation Values for Observables; Application to the Forced Harmonic Oscillator; Particles Interacting Through an Intermediate Oscillator; Space Time Approach to Non-Relativistic Quantum Mechanics; The Lagrangian in Quantum Mechanics..
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The book clearly and concisely explains the basic principles of Lagrangian dynamicsand provides training in the actual physical and mathematical techniques of applying Lagrange's equations, laying the foundation for a later study of topics that bridge the gap between classical and quantum physics, engineering, chemistry and applied mathematics, and for practicing scientists and engineers.

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"An Introduction to Lagrangian Mechanics" begins with a proper historical perspective on the Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d'Alembert that preceded Hamilton's formulation of the Principle of Least Action, from which the Euler-Lagrange equations of motion are derived.Other additional topics not traditionally presented in undergraduate textbooks include the treatment of constraint forces in Lagrangian Mechanics; Routh's procedure for Lagrangian systems with symmetries; the art of numerical analysis for physical systems; variational formulations for several continuous Lagrangian systems; an introduction to elliptic functions with applications in Classical Mechanics; and Noncanonical Hamiltonian Mechanics and perturbation theory. This textbook is suitable for undergraduate students who have acquired the mathematical skills needed to complete a course in Modern Physics..
Price: $38.00 [Notify me when price goes down.]

This is a text on Hamiltionian and Lagrangian Dynamics aimed at the student who has just finished the calculus sequence. Such a student has probably heard of relativity and quantum mechanics, but has not heard of Hamiltonian or Lagrangian Dynamics. A natural reaction to something new is "If it's so important, why haven't I heard of it before." Such a student deserves an answer. Hamiltonian and Lagrangian Dynamics are important because they make problems easy that would otherwise be very, very painful. Also, it is these formalisms, not that of Newton, that still has meaning in quantum mechanics. And, on a spiritual level, this material explains the underlying reasons for why things are the way they are, in both quantum land and on the classical level. A very large amount of physics ends up tracing its way back to this material. This book distinguishes itself from others by developing Hamiltonian mechanics before Lagrangian mechanics. The Hamiltonian is more or less what you would call energy, so it is closer to the intuition than the Lagrangian, so it puts the reader on firmer ground intuitively and "schematically" than the usual approach. This book has a much stronger geometric character than is typical of books on this subject. And so many of the exercises are unusually "artistic" in the sense of asking the student to draw pictures, or accompany calculations with drawings. This the reason for the subtitle "A Coloring Book for Young Physicists." I don't mean that this is meant for elementary school age students. But I do mean that this book is intended to be a core intimate exploratory experience, like a coloring book can be. Find out what things are, and find out what they feel like on the tip of your crayon. There is a split in the literature of classical mechanics. The mathematical literature is not accessible to the undergraduate, and seems too general and abstract to be about physics,.
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Many important physical systems have input-output properties related to the conservation, dissipation and transport of energy. The theory surrounding such "dissipative properties" may be used as a framework for the design and analysis of control systems. The consideration of dissipativity is useful – and may be indispensable – for control applications like robotics, active vibration damping and circuit theory and for some control techniques themselves: adaptive, nonlinear-H-infinity , and inverse-optimal control among them.

Dissipative Systems Analysis and Control (second edition) presents a fully revised and expanded treatment of dissipative systems theory, constituting a self-contained, advanced introduction for graduate students, researchers and practising engineers. It examines linear and nonlinear systems with examples of both in each chapter; some infinite-dimensional and nonsmooth examples are also included. Throughout, emphasis is placed on the use of the dissipative properties of a system for the design of stable feedback control laws. The theory is consistently substantiated by experimental results and by reference to its application in illustrative physical cases (Lagrangian and Hamiltonian systems and passivity-based and adaptive controllers are covered thoroughly).

The second edition is substantially reorganized both to accommodate new material and to enhance its pedagogical properties. Some of the changes introduced are:

• Complete proofs of the main theorems and lemmas.

• The Kalman–Yakubovich–Popov Lemma for non-minimal realizations, singular systems, and discrete-time systems (linear and nonlinear).

• Passivity of nonsmooth systems (differential inclusions, variational inequalities, Lagrangian systems with complementarity conditions).

• Sections on optimal control and H-infinity theory.

• An enlarged bibliography with more than 550 references, and an augmented index with more than 500 entries.

• An improved appendix with introductions to viscosity solutions, Riccati equations and some useful matrix algebra.

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Remarkable progress has recently been made in the application of quantumtrajectories as the computational tool for solving quantum mechanical problems. This is the first book to present these developments in the broader context of the hydrodynamical formulation of quantum dynamics. In addition to a thorough discussion of the quantum trajectory equations of motion, there is considerable material that deals with phase space dynamics, adaptive moving grids, electronic energy transfer, and trajectories for stationary states.

On the pedagogical side, a number of sections of this book will be accessible to students who have had an introductory quantum mechanics course. There is also considerable material for advanced researchers, and chapters in the book cover both methodology and applications. The book will be useful to students and researchers in physics, chemistry, applied math, and computational dynamics.

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This book has sufficient material for two full-length semester courses in advanced engineering dynamics. As such it contains two tracks (which overlap in places). During the first course a Newton-Euler approach is used, followed by a Lagrangian approach in the second. In discussing rotations for the second course, time constraints permit a detailed discussion of only the Euler angle parameterization of a rotation tensor from Chapter 6 and a brief mention of the examples on rigid body dynamics discussed in Chapter 9. The text includes invaluable exercises at the end of each chapter that are highly structured and intended as a self-study aid. Validated solutions are provided, many of which can be performed in simulation using MATLAB® or Mathematica®..
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This long-awaited book by two of the foremost researchers and writers in the field is the first part of a treatise that covers the subject in breadth and depth, paying special attention to the historical origins, partly in applications, e.g. from geometrical optics, of parts of the theory. A variety of aids to the reader is provided: besides the very detailed table of contents, an introduction to each chapter, section and subsection, an overview of the relevant literature (in Vol. 2) plus the references in the Scholia to each chapter, in the (historical) footnotes, and in the bibliography, and finally an index of the examples used throughout the book. Both individually and collectively these volumes have already become standard references..
Price: $129.00 [Notify me when price goes down.]

This long-awaited book by two of the foremost researchers and writers in the field is the first part of a treatise that will cover the subject in breadth and depth, paying special attention to the historical origins, partly in applications, e.g. from geometrical optics, of parts of the theory. A variety of aids to the reader are provided: the detailed table of contents, an introduction to each chapter, section and subsection, an overview of the relevant literature (in Vol. 2) plus the references in the Scholia to each chapter, in the (historical) footnotes, and in the bibliography, and finally an index of the examples used throughout the book. Later volumes will deal with direct methods and regularity theory. Both individually and collectively these volumes will undoubtedly become standard references..
Price: $135.20 [Notify me when price goes down.]