- Series: Dover Books on Physics (Book 4)
- Paperback: 464 pages
- Publisher: Dover Publications; 4th Revised ed. edition (March 1, 1986)
- Language: English
- ISBN-10: 9780486650678
- ISBN-13: 978-0486650678
- ASIN: 0486650677
- Product Dimensions: 5.4 x 0.9 x 8.5 inches
- Shipping Weight: 1.3 pounds (View shipping rates and policies)
- Average Customer Review: 39 customer reviews
- Amazon Best Sellers Rank: #119,312 in Books (See Top 100 in Books)
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The Variational Principles of Mechanics (Dover Books on Physics) 4th Revised ed. Edition
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Top customer reviews
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?? These are my reasons:
1) From a historical point of view, Analytical Mechanics was developed by Continental Mathematicians like Maupertuis, Euler, D'Alembert and Lagrange as a rival system to the Newtonian one exposed in the Principia Mathematica. Newton used vectors and potentials. Euler and Lagrange employed the Principle of Least Action.
2) It was Analytical Mechanics the first to develop the principle of energy conservation. Even when this principle in its general form was developed by Wilhelm von Helmholtz in 1847, the conservation of the sum of kinetic and potential energy was well known to Euler a century earlier.
3) The concept of phase space is very important in Thermodynamics. In fact, the definition of entropy given by Ludwig Boltzmann refers to the logarithm of a volume in phase space. Liouville theorem, which states the conservation of such phase space volumes, is very usefull today in black hole thermodynamics.
4) The quantum-mechanical interpretation of the Principle of Least Action given by Richard Feynmann was a fundamental contribution in the development of Quantum Field Theory, so any student who desires to progress in this field, must have substantial knowledge of Analytical Mechanics.
So, to all of you that eventually decide to buy this book, I wish you a good reading.
I consider Lanczos's work a work of art. This is not in detriment of its scientific and mathematical value; on the contrary, it means that he was able in his "Principles of Variational Mechanics" (as well as in his "Discourse on Fourier Series") to add beauty to scientific and mathematical rigor. This happen so seldom that I cannot but to strongly recommend this extraordinary book.
Lanczos teaches you not only the subject matter, but a way to think about the subject matter in a deeper way.
Einstein thought highly of Cornelius Lanczos. If you read his books you'll know why.
Analytical mechanicians, by their very nature, are a philosophical lot. Maybe its because they assume everything will fit perfectly in their models or maybe its an outgrowth of their expectation of a rational natural order, regardless, this is a book tailored to that sort of mind. Recent texts in analytical mechanics, although tremendously useful for their pedagogical value, are usually quite cut and dry. There have been, in the last few years, exceptions to this but many of these spend more time attacking fellow researchers/scientists and dissecting competing views in the theory (quite reminiscent of traditional philosophers!) rather than attempt to give meaning through discussion.
Lanczos is a great antidote for this. This is really an exquisite work that anyone in analytical mechanics will readily appreciate. If you want to know how to do analytical mechanics, look elsewhere. If you want to know the soul of analytical mechanics, look nowhere else.
It must be noted that since many aspects of analytical mechanics are "point of view" rather than fact, some preferences of Lanczos may not be the only view or even orthodox. An example of this would be contemporaneous variations (Lanczos does not accept). Even though they are controversial in some sense, they do provide elegant alternatives of the proofs of several basic results in Hamiltonian mechanics.
Most recent customer reviews
The entire book feels like an informal conversation.