Table of Contents

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[is 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

About the Author

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.

Reviews

Jennifer Coopersmith has written a most welcome book, the first historically and philosophically motivated full study since two classics written nearly a half-century ago... [She] has attempted and succeeded admirably I believe in her aim to write a modern book on the history and philosophy of the action principles, as well as to give the technical details.
*Chris Gray, American Journal of Physics*

Any careful reader of this book will seek out the monograph without fail and benefit from its perusal... I have no hesitations in recommending this book to any physical scientist or engineer who wants to understand variational principles better.
*M. P. Gururajan, Contemporary Physics*

Recommended.
*CHOICE*

[C]ontagious enthusiasm and a sense of humour unusual in this kind of literature ... The first part is excellent reading for anybody with an interest in the history and philosophy of science. I also recommend the book to students in physics and mathematics who are willing to dig deeper into this subject after taking classes in analytical mechanics, and I believe that it is accessible to any student in STEM disciplines. Practitioners in physics from any sub-discipline will enjoy a refresh and a different point of view that puts their tools of the trade in a broader context.
*Andrea Giammanco, CERN Courier*

Inspired by the monumental work of Lanczos, Jennifer Coopersmith has constructed a beautiful exposition of the philosophical basis underlying classical mechanics. It has enough technical meat to be interesting to an expert, while remaining accessible to a novice.
*Gerald Jay Sussman, Panasonic Professor of Electrical Engineering, Massachusetts Institute of Technology*

This is a well written and comprehensible presentation of some of the most fascinating and fundamental principles which theoretical physics has uncovered. The author has done a great job in making accessible 'as if-laws' to a broader audience.
*Helmut Pulte, Ruhr University Bochum, Germany*

This book has a general audience: every practicing physicist -- and a specific audience: every physics textbook writer. Envision and teach physics powerfully and directly with energy, action, and the Principle of Least Action.
*Edwin F. Taylor, Senior Research Scientist Emeritus, Massachusetts Institute of Technology*