Jennifer Coopersmith

The Lazy Universe (eBook, PDF)

An Introduction to the Principle of Least Action

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Oxford University Press
• Seitenzahl: 272
• Erscheinungstermin: 28. April 2017
• Englisch
• ISBN-13: 9780191060724
• Artikelnr.: 48794329

Autorenporträt

Jennifer Coopersmith took her PhD in nuclear physics from the University of London, and was later a research fellow at TRIUMF, University of British Columbia. She was for many years an associate lecturer for the Open University (London and Oxford), and was then a tutor on astrophysics courses at Swinburne University of Technology in Melbourne while based at La Trobe University in Bendigo, Victoria. She now lives in France.

Inhaltsangabe

1: Introduction
2: Antecedents
3: Mathematics and physics preliminaries
4: The Principle of Virtual Work
5: D'Alembert's Principle
6: Lagrangian Mechanics
7: Hamiltonian Mechanics
8: The whole of physics
9: Final words
Appendices
A1.1: Newton's Laws of Motion
A3.1: Reversible Displacements
A2.1: Portraits of the physicists
A6.1: Worked examples in Lagrangian Mechanics
A6.2: Proof that T is a function of v²
A6.3: Energy conservation and the homogeneity of time
A6.4: The method of Lagrange Multipliers
A6.5: Generalized Forces
A7.1: Hamilton's Transformation, Examples
A7.2: Demonstration that the p¿s are independent coordinates
A7.3: Worked examples in Hamiltonian Mechanics
A7.4: Incompressibility of the phase fluid
A7.5: Energy conservation in extended phase space
A7.6: Link between the action, S, and the 'circulation'
A7.7: Transformation equations linking p and q via S
A7.8: Infinitesimal canonical transformations
A7.9: Perpendicularity of wavefronts and rays
A7.10: Problems solved using the Hamilton-Jacobi Equation
A7.11: Quasi refractive index in mechanics
A7.12: Einstein's link between Action and the de Broglie waves