Download PDF The Variational Principles of Mechanics Dover Books on Physics Cornelius Lanczos 9780486650678 Books
Download As PDF : The Variational Principles of Mechanics Dover Books on Physics Cornelius Lanczos 9780486650678 Books
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.
Download PDF The Variational Principles of Mechanics Dover Books on Physics Cornelius Lanczos 9780486650678 Books
"As an engineer, I've never been content with the formalized approaches to teaching mathematics and physics. I find derivation upon derivation of of equation and mathematical contrivances to be dull without having a deeper more intuitive grasp of what the equations seek to describe.
This book, by Cornelius Lanczos to put it simply, is a physics book which approaches the subject by relaying the intuitive grasp first, and then supplementing the intuition with formula.
I purchased this book with absolutely no background in Lagrangian Mechanics. I have but the faintest conception of what a Hamiltonian is. But even I find the book accessible enough to be wonderfully engaging.
Let me share a quote to illustrate how the book tends to approach its explanations:
"Since motion is by its very nature a directed phenomenon, it seems puzzling that two scalar quantities should be sufficient to determine the motion...And yet it is a fact that these two fundamental scalars contain the complete dynamics of even the most complicated material system, provided they are used as the basis of a principle rather than of an equation"
In my opinion, to really learn the meaning behind the equations, to learn rather the principles behind the equations themselves is really that deeper understanding that every scientist and engineer only comes to understand over the course of a lifetime. I can scarcely believe that we have the benefit of a lifetime's worth of understanding of advanced physics so eloquently delineated here. This is an absolute gem of a book and I cannot recommend it more highly."
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The Variational Principles of Mechanics Dover Books on Physics Cornelius Lanczos 9780486650678 Books Reviews :
The Variational Principles of Mechanics Dover Books on Physics Cornelius Lanczos 9780486650678 Books Reviews
- As an engineer, I've never been content with the formalized approaches to teaching mathematics and physics. I find derivation upon derivation of of equation and mathematical contrivances to be dull without having a deeper more intuitive grasp of what the equations seek to describe.
This book, by Cornelius Lanczos to put it simply, is a physics book which approaches the subject by relaying the intuitive grasp first, and then supplementing the intuition with formula.
I purchased this book with absolutely no background in Lagrangian Mechanics. I have but the faintest conception of what a Hamiltonian is. But even I find the book accessible enough to be wonderfully engaging.
Let me share a quote to illustrate how the book tends to approach its explanations
"Since motion is by its very nature a directed phenomenon, it seems puzzling that two scalar quantities should be sufficient to determine the motion...And yet it is a fact that these two fundamental scalars contain the complete dynamics of even the most complicated material system, provided they are used as the basis of a principle rather than of an equation"
In my opinion, to really learn the meaning behind the equations, to learn rather the principles behind the equations themselves is really that deeper understanding that every scientist and engineer only comes to understand over the course of a lifetime. I can scarcely believe that we have the benefit of a lifetime's worth of understanding of advanced physics so eloquently delineated here. This is an absolute gem of a book and I cannot recommend it more highly. - 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 work to Einstein's equivalence principle and the origin of the gravitational redshift of spectral lines. The book contains very little material on the Newtonian, vector mechanics, being entirely devoted to the Lagrangian and Hamiltonian approaches to mechanics.
The book provides a perfect introduction to the foundations of the all important principle of least action that pervades all of modern physics. In this regard, a nice companion to Lanczos' book is the treatise by W. Yourgrau and S. Mandelstam, "Variational Principles in Dynamics and Quantum Theory."
One major "functionality" of Lanczos' book is to bridge the gap between our modern way of thinking and that of the classics. Anyone who has already tried to read the 1762 papers by Lagrange on Miscellanea Taurinensia or the 1834-1835 papers by Hamilton on the Phil. Trans. Royal Soc. knows that the classical literature is difficult to follow, part because of old-fashioned notation, part because we lack (well, at least I lack) the spirit of the times, making it difficult to understand some seemingly byzantine questions that the authors pose and ponder on in some of their (sometimes rather lenghty) writings. The book by Lanczos helps a lot both in terms of notation and ideas.
I totally disagree with those that try to compare Lanczos' and Feynman's styles. Lanczos is seriously concerned with the history of the ideas, their evolution, and interpretations. There is nothing like that in Feynman's "The strange theory of light and matter," or in his "The character of physical law," and very little of it in his lectures on physics. Actually, Feynman pays very little credit to the historical development of the subjects. I am not saying that he personally does not recognize the credits, only that he does not communicate it. He admittedly has a "do it yourself" (or "did it myself") attitude towards physics, while Lanczos has a visible admiration for the greatness of his subject (without being cheesy) and is sensitive to its philosophical nuances and implications. I feel the difference between the two is like the difference between getting trained and getting educated.
In summary a must have in anyone's scientific library (unless you are an undergrad student cramming for your finals). - Hamilton said of Lagrange's Analytical Mechanics that it was a "scientific poem" and considered Lagrange "the Shakespeare of Mechanics."
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.
