The Variational Principles of Mechanics

by Cornelius Lanczos

Book Overview

Analytical mechanics is, of course, a topic of perennial interest and usefulness in physics and engineering, a discipline that boasts not only many practical applications, but much inherent mathematical beauty. Unlike many standard textbooks on advanced mechanics, however, this present text eschews a primarily technical and formalistic treatment in favor of a fundamental, historical, philosophical approach. As the author remarks, there is a tremendous...

• Format: Paperback
• Language: English
• ISBN: 0486650677
• ISBN13: 9780486650678
• Release Date: March 1986
• Publisher: Dover Publications
• Length: 464 Pages
• Weight: 1.08 lbs.
• Dimensions: 0.9" x 5.4" x 8.5"

Customer Reviews

Timeless classic, masterful ...

If you ask 10 PhD scientists: "Why is Schrodinger's Equation complex?" (contains the square-root of minus one), 9 out of 10 won't be able to give you the correct answer. It has little to do with taking the root of negative numbers. After reading Lanczos you will know it has do with "space" and what is a proper physical law. (Now you have to read the book to parse this sentence. Good.) This is one of many wonderful insights Lanczos provides; with humor, wonder and crystal clarity. This is not a 'text book' on mechanics, you will get more out of it if you are familiar with the subject. He gives you understanding, not technique. It is as if you can hum a few tunes. Reading Lanczos is experiencing the entire opera for the first time. Now you know the full story, how each aria is a part of the fabric; how each fits in the situation, the motivation behind it. The tunes you liked become richer, more profound, they are connected. The next time you sing you fancy you are a Caruso, a Puccini. It is so rare to encounter a master who is also a gifted writer. Some reviewers compare Lanczos to Feynman's Lectures, I agree partly. Lanczos is more literate and much more humble. Feynman is so busy being the genius from Brooklyn that his exposition is choppy and uneven. Lanczos is a better organizer and writer.

A Treasure

Surely Lanzcos is one of the few educators that compare to Feynman. This book presents an exceptionally lucid and engaging development of the main variational principles of mechanics with the discussion of Noethers theorem being the most cogent I've seen. While the problems may not be exceedingly difficult, this is because the problems are intended to illuminate the ideas under discussion. Lanzcos divides mechanics very roughly into two camps, the vectorial/one-form viewpoint versus variational/analytical view. Since Lanzcos aspires to the variational view, the criticism concerning the lack of discussion of vectorial/one-form is rather moot and explains why there are not a great number of drawings. While this may be a problem for some, in my view figures can convey a false sense of understanding. This is not a work that one can skim, it expects considerable reflection on the contents. We all differ in our needs and wants but in my view, this exposition exudes a truly infectious sense of wonder that such simple ideas could be so powerful and beautiful. But since no one book in this field may suffice for all one might also consider "Mechanics: From Newton's Laws to Deterministic Chaos" by Florian Scheck which admittedly covers mathematical methods that Lanzcos does not yet fails to capture the essence of the ideas as well as the Lanzcos text does.

Lucid and elegant -- a true classic

Lanczos' book is a compelling analysis of the principles of Lagrangian and Hamiltonian mechanics. It reminds me a bit of Feyman's Lectures on Physics because it focuses on the motivating principles behind advanced mechanics. In an elegant and flowing style, Lanczos guides the reader through a walking tour of the principles of mechanics, peppered with historical footnotes. If you understand how to use mechanics, but want to understand how the underlying principles are developed, this is an excellent choice.

A Joy to Read

As another reviewer states, the book is somewhat broader than the title suggests. The chapters of the book are 1. The Basic Concepts of Analytical Mechanics 2. The Calculus of Variations 3. The Principle of Virtual Work 4. D'Alembert's Principle 5. The Langrangian Equations of Motion 6. The Canonical Equations of Motion 7. Canonical Transformations 8. The Partial Diffirential Equation of Hamilton-Jacobi 9. Relativistic Mechanics 10. Historical Survey 11. Mechanics of the ContinuaThere are a few examples and problems in the text, but I certainly wished for more to help illustrate concepts.The author conveys in every chapter a strong reverence of the aesthetic value of the material and does an excellent job of showing how the themes of the analytic approach to clasical mechanics are preserved in relativity and quantum mechanics.

Classical Treatment of Variational Principles of Mechanics

Cornelius Lanczos is the figure of paramount importance in the fields of Theoretical Physics, Applied Mathematics and Numerical Algorithms. In his lucid treatment of variational calculus Lanczos conscisely sums up the ideas that form foundation of the mathematical apparatus of contemporary fundamental physics. A must reading for any Graduate Student in Physics.