Variational Principles of Mechanics (Mathematical Expositions) [Paperback]

Cornelius Lanczos (Author)

Book Description

Publication Date: February 25, 1971 | Series: Mathematical Expositions

Philosophic, less formalistic approach to perennially important field of analytical mechanics. Model of clear, scholarly exposition at graduate level with coverage of basic concepts, calculus of variations, principle of virtual work, equations of motion, relativistic mechanics, much more. First inexpensive paperbound edition. Index. Bibliography.

--This text refers to an alternate Paperback edition.

Product Details

• Paperback: 448 pages
• Publisher: University of Toronto Press; 4th edition (February 25, 1971)
• Language: English
• ISBN-10: 0802017436
• ISBN-13: 978-0802017437
• Average Customer Review: 4.8 out of 5 stars  See all reviews (18 customer reviews)
• Amazon Best Sellers Rank: #3,217,222 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

52 of 53 people found the following review helpful:

5.0 out of 5 stars A Treasure, April 17, 2003

By 

Edward H. Welbon "epiphenomenalist" (Austin, Tx United States) - See all my reviews
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This review is from: The Variational Principles of Mechanics (Dover Books on Physics) (Paperback)

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.

39 of 40 people found the following review helpful:

5.0 out of 5 stars Timeless classic, masterful ..., December 19, 2006

By 

S. K. Hoo "freelance707" (Silicon ValleySan Jose, CA USA) - See all my reviews
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This review is from: The Variational Principles of Mechanics (Dover Books on Physics) (Paperback)

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.

19 of 19 people found the following review helpful:

5.0 out of 5 stars Lucid and elegant -- a true classic, January 28, 2002

By 

"erzielin" (Chicago, IL United States) - See all my reviews

This review is from: The Variational Principles of Mechanics (Dover Books on Physics) (Paperback)

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.