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The Variational Principles of Mechanics (Dover Books on Physics) [Paperback]

Cornelius Lanczos
4.8 out of 5 stars  See all reviews (26 customer reviews)

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Book Description

March 1, 1986 0486650677 978-0486650678 4

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 treasure of philosophical meaning" behind the great theories of Euler and Lagrange, Hamilton, Jacobi, and other mathematical thinkers.
Well-written, authoritative, and scholarly, this classic treatise begins with an introduction to the variational principles of mechanics including the procedures of Euler, Lagrange, and Hamilton.
Ideal for a two-semester graduate course, the book includes a variety of problems, carefully chosen to familiarize the student with new concepts and to illuminate the general principles involved. Moreover, it offers excellent grounding for the student of mathematics, engineering, or physics who does not intend to specialize in mechanics, but wants a thorough grasp of the underlying principles.
The late Professor Lanczos (Dublin Institute of Advanced Studies) was a well-known physicist and educator who brought a superb pedagogical sense and profound grasp of the principles of mechanics to this work, now available for the first time in an inexpensive Dover paperback edition. His book will be welcomed by students, physicists, engineers, mathematicians, and anyone interested in a clear masterly exposition of this all-important discipline.


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The Variational Principles of Mechanics (Dover Books on Physics) + Calculus of Variations (Dover Books on Mathematics) + Differential Geometry (Dover Books on Mathematics)
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Product Details

  • Series: Dover Books on Physics (Book 4)
  • Paperback: 418 pages
  • Publisher: Dover Publications; 4 edition (March 1, 1986)
  • Language: English
  • ISBN-10: 0486650677
  • ISBN-13: 978-0486650678
  • Product Dimensions: 6.3 x 8.3 x 0.9 inches
  • Shipping Weight: 1 pounds (View shipping rates and policies)
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (26 customer reviews)
  • Amazon Best Sellers Rank: #109,924 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
79 of 81 people found the following review helpful
5.0 out of 5 stars A Treasure April 17, 2003
Format: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.
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76 of 81 people found the following review helpful
5.0 out of 5 stars Timeless classic, masterful ... December 19, 2006
Format: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.
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34 of 35 people found the following review helpful
5.0 out of 5 stars Lucid and elegant -- a true classic January 28, 2002
Format: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.
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30 of 31 people found the following review helpful
5.0 out of 5 stars A pedagogical introduction into analytical mechanics October 11, 2009
Format:Paperback|Verified Purchase
Before reading this book, I knew almost nothing about analytical mechanics. My first text books taught Physics from a Newtonian approach, using mostly vectors and potentials. So, the first time I encountered Lagrangians and Hamiltonians I could not understand what these concepts meant. Because of that many areas of Theoretical Physics were forbidden for me: Phase and configuration space, Noether's theorem, Hilbert relativistic equations, Feynman quantum-mechanical interpretation of the principle of least action, and so on.

So, two years ago, I decided to buy this book. And what I encountered? A systematical and pedagogical approach to analytical mechanics, which enabled me to acquire the fundamentals of the subject.

For me, the most interesting features of this book are the following:

1) It explains the differences between VARIATION and DIFFERENTIATION, something that most books in the subject, leave behind.
2) It explains clearly D'Alembert Principle and the Principle of Virtual Work.
3) From those principles he derives the Principle of Least Action, using just elemental calculus.
4) He introduces the reader in Legendre's transformation and the relations between the two fundamental quantities of Analytical mechanics: Lagrangian and Hamiltonian.
5) You get the equations of movement corresponding to those quantities: Euler-Lagrange (Lagrangian) and canonical (Hamiltonian) equations.
6) A powerful insight in Configuration and Phase Spaces is given, including the wonderful Liouville's theorem.
7) Lanczos shows the analogies between Optics and Mechanics when he explains the Hamilton-Jabobi equations.

So, why to learn Analytical Mechanics and why to buy this book??
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20 of 21 people found the following review helpful
5.0 out of 5 stars A Joy to Read April 14, 2001
By A Customer
Format:Paperback
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 Continua
There 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.
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Most Recent Customer Reviews
5.0 out of 5 stars A work of art
Hamilton said of Lagrange's Analytical Mechanics that it was a "scientific poem" and considered Lagrange "the Shakespeare of Mechanics. Read more
Published 4 months ago by Marcial Losada
5.0 out of 5 stars Excellent book!
Excellent book, very clear, describing complex information in a very appealing manner. To introduce each concept, the author starts with a description using words and gets to very... Read more
Published 5 months ago by ileana murgueitio
5.0 out of 5 stars A classic
This is the classic reference for anybody who is interested in understanding variational principles. Read more
Published 5 months ago by Ismael Castelazo
4.0 out of 5 stars Excellent Light Reading for Post Graduate Physicists
Here is a funny thing: Objects in motion tend to move in such a way that a particular integral over the path of the motion, an integral only involving the kinetic energy and work... Read more
Published 5 months ago by Jonathan V. Toups
5.0 out of 5 stars Quite simply the best
This is probably my favorite book of all time. It is a very rich treatise on analytical mechanics. It does a good job of explaining the philosophy and motivations of the physics,... Read more
Published 11 months ago by tmchale
5.0 out of 5 stars The best book on the subject!
What could be said more?
If you read it carefully, you begin to feel the subject more seeply. I guarrantee
Published 16 months ago by Wojciech Karaś
5.0 out of 5 stars Really great book, especially for readers who are not mathematicians
It is a great introduction for engineering students. These topics are often teached in a shortened form and they often unclear for many students. Read more
Published 17 months ago by Jiri Brozovsky
5.0 out of 5 stars Insightful, a necessary reading
It really takes you there. Very insightful and complete. Also, for those who like to know how things developed this book is a gem. Read more
Published 18 months ago by Luciana Veglia
5.0 out of 5 stars Perfect bridge between the classical and the XXth century physics
Lanczos' "Variational Principles of Mechanics" is an erudite piece of work that basically reconstructs the science of analytical mechanics bottom up, from the principle of virtual... Read more
Published on November 12, 2011 by J. R. G. Mendonca
5.0 out of 5 stars The soul of variational mechanics
This is one of the best books I have ever laid my hands on. Lanczos does a tremendous job of blending mathematics, physics, intuition and philosophy. Read more
Published on June 28, 2011 by Ismail Hameduddin
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