The Lazy Universe

Author: Jennifer Coopersmith
Publisher: Oxford University Press
ISBN: 0191060720
File Size: 13,97 MB
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This is a rare book on a rare topic: it is about 'action' and the Principle of Least Action. A surprisingly well-kept secret, these ideas are at the heart of physical science and engineering. Physics is well known as being concerned with grand conservatory principles (e.g. the conservation of energy) but equally important is the optimization principle (such as getting somewhere in the shortest time or with the least resistance). The book explains: why an optimization principle underlies physics, what action is, what `the Hamiltonian' is, and how new insights into energy, space, and time arise. It assumes some background in the physical sciences, at the level of undergraduate science, but it is not a textbook. The requisite derivations and worked examples are given but may be skim-read if desired. The author draws from Cornelius Lanczos's book "The Variational Principles of Mechanics" (1949 and 1970). Lanczos was a brilliant mathematician and educator, but his book was for a postgraduate audience. The present book is no mere copy with the difficult bits left out - it is original, and a popularization. It aims to explain ideas rather than achieve technical competence, and to show how Least Action leads into the whole of physics.

The Lazy Universe

Author: Jennifer Coopersmith
Publisher: Oxford University Press
ISBN: 0191060739
File Size: 72,39 MB
Format: PDF, ePub, Docs
Read: 3438
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This is a rare book on a rare topic: it is about 'action' and the Principle of Least Action. A surprisingly well-kept secret, these ideas are at the heart of physical science and engineering. Physics is well known as being concerned with grand conservatory principles (e.g. the conservation of energy) but equally important is the optimization principle (such as getting somewhere in the shortest time or with the least resistance). The book explains: why an optimization principle underlies physics, what action is, what `the Hamiltonian' is, and how new insights into energy, space, and time arise. It assumes some background in the physical sciences, at the level of undergraduate science, but it is not a textbook. The requisite derivations and worked examples are given but may be skim-read if desired. The author draws from Cornelius Lanczos's book "The Variational Principles of Mechanics" (1949 and 1970). Lanczos was a brilliant mathematician and educator, but his book was for a postgraduate audience. The present book is no mere copy with the difficult bits left out - it is original, and a popularization. It aims to explain ideas rather than achieve technical competence, and to show how Least Action leads into the whole of physics.

The Lazy Universe

Author: Jennifer Coopersmith
Publisher: Oxford University Press
ISBN: 0198743041
File Size: 56,12 MB
Format: PDF, Docs
Read: 4710
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This book is about 'action' and the Principle of Least Action. These ideas are at the heart of physical science and engineering. Physics is well known as being concerned with grand conservatory principles (e.g. the conservation of energy) but equally important is the optimization principle (such as getting somewhere in the shortest time or with the least resistance). The book explains: why an optimization principle underlies physics, what action is, what 'the Hamiltonian' is, and how new insights into energy, space, and time arise. It assumes some background in the physical sciences, at the level of undergraduate science, but it is not a textbook. The requisite derivations and worked examples are given but may be skim-read if desired. The author draws from Cornelius Lanczos's book 'The Variational Principles of Mechanics' (1949 and 1970). The present book is no mere copy with the difficult bits left out. It aims to explain ideas rather than achieve technical competence, and to show how Least Action leads into the whole of physics.

The Principle Of Least Action

Author: Alberto Rojo
Publisher: Cambridge University Press
ISBN: 0521869021
File Size: 64,99 MB
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This text brings history and the key fields of physics together to present a unique technical discussion of the principles of least action.

The Variational Principles Of Mechanics

Author: Cornelius Lanczos
Publisher: Courier Corporation
ISBN: 0486134709
File Size: 11,61 MB
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Philosophic, less formalistic approach to analytical mechanics offers model of clear, scholarly exposition at graduate level with coverage of basics, calculus of variations, principle of virtual work, equations of motion, more.

Energy The Subtle Concept

Author: Jennifer Coopersmith
Publisher: OUP Oxford
ISBN: 0191057509
File Size: 42,40 MB
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Energy is at the heart of physics and of huge importance to society and yet no book exists specifically to explain it, and in simple terms. In tracking the history of energy, this book is filled with the thrill of the chase, the mystery of smoke and mirrors, and presents a fascinating human-interest story. Moreover, following the history provides a crucial aid to understanding: this book explains the intellectual revolutions required to comprehend energy, revolutions as profound as those stemming from Relativity and Quantum Theory. Texts by Descartes, Leibniz, Bernoulli, d'Alembert, Lagrange, Hamilton, Boltzmann, Clausius, Carnot and others are made accessible, and the engines of Watt and Joule are explained. Many fascinating questions are covered, including: - Why just kinetic and potential energies - is one more fundamental than the other? - What are heat, temperature and action? - What is the Hamiltonian? - What have engines to do with physics? - Why did the steam-engine evolve only in England? - Why S=klogW works and why temperature is IT. Using only a minimum of mathematics, this book explains the emergence of the modern concept of energy, in all its forms: Hamilton's mechanics and how it shaped twentieth-century physics, and the meaning of kinetic energy, potential energy, temperature, action, and entropy. It is as much an explanation of fundamental physics as a history of the fascinating discoveries that lie behind our knowledge today.

Lagrangian Interaction

Author: Noel Doughty
Publisher: CRC Press
ISBN: 0429973160
File Size: 62,13 MB
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This book is an introduction to Lagrangian mechanics, starting with Newtonian physics and proceeding to topics such as relativistic Lagrangian fields and Lagrangians in General Relativity, electrodynamics, Gauge theory, and relativistic gravitation. The mathematical notation used is introduced and explained as the book progresses, so it can be understood by students at the undergraduate level in physics or applied mathmatics, yet it is rigorous enough to serve as an introduction to the mathematics and concepts required for courses in relativistic quantum field theory and general relativity.

Perfect Form

Author: Don Stephen Lemons
Publisher: Princeton University Press
ISBN: 9780691026633
File Size: 74,19 MB
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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.

Variational Principles

Author: B. L. Moiseiwitsch
Publisher: Courier Corporation
ISBN: 0486150496
File Size: 53,44 MB
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This text shows how variational principles are used to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities that arise in the theory of scattering. 1966 edition.

Noise Theory And Application To Physics

Author: Philippe Réfrégier
Publisher: Springer Science & Business Media
ISBN: 0387225269
File Size: 16,89 MB
Format: PDF
Read: 2449
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This is a unique approach to noise theory and its application to physical measurements that will find its place among the graduate course books. In a very systematic way, the foundations are laid and applied in a way that the book will also be useful to those not focusing on optics. Exercises and solutions help students to deepen their knowledge.