81 of 86 people found the following review helpful:
5.0 out of 5 stars
Symmetries to make you weep, August 3, 2005
This review is from: Mechanics, Third Edition: Volume 1 (Course of Theoretical Physics) (Paperback)
If physicists could weep, they would weep over this book. The book is devastingly brief whilst deriving, in its few pages, all the great results of classical mechanics. Results that in other books take take up many more pages. I first came across Landau's mechanics many years ago as a brash undergrad. My prof at the time had given me this book but warned me that it's the kind of book that ages like wine. I've read this book several times since and I have found that indeed, each time is more rewarding than the last.
The reason for the brevity is that, as pointed out by previous reviewers, Landau derives mechanics from symmetry. Historically, it was long after the main bulk of mechanics was developed that Emmy Noether proved that symmetries underly every important quantity in physics. So instead of starting from concrete mechanical case-studies and generalising to the formal machinery of the Hamilton equations, Landau starts out from the most generic symmetry and dervies the mechanics. The 2nd laws of mechanics, for example, is derived as a consequence of the uniqueness of trajectories in the Lagragian. For some, this may seem too "mathematical" but in reality, it is a sign of sophisitication in physics if one can identify the underlying symmetries in a mechanical system. Thus this book represents the height of theoretical sophistication in that symmetries are used to derive so many physical results.
The difficulty with this approach, and the reason why this book is not a beginner's book, is that to the follow symmetric arguments, one really has to have already mastered vector calculus. Ideally, you should be able to transform coordinate in your sleep, perform integrals without missing a beat, whether they be line, area, or path, and differentiate functions in many dimensions. The arguments are not sloppy, as some have claimed - it only seems so if you have not mastered vector calculus.
Tradition says that in Plato's academy was engraved the phrase, "Let no one ignorant of geometry enter here", so should the modern theoretical physicist, with Landau's bible in hand, march under the arches engraved with the words "Let no one ignorant of symmetry enter here".
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41 of 44 people found the following review helpful:
5.0 out of 5 stars
Better than Goldstein, December 11, 1999
This review is from: Mechanics, Third Edition: Volume 1 (Course of Theoretical Physics) (Paperback)
Classical Mechanics by H. Goldstein was the assigned text for a senior year course on CM. In all fairness, Goldstein does introduce tools and concepts useful to more advanced study in the subject, so I would turn to G. for a second reading on these topics. He also discusses the connections between classical to quantum mechanics. Nevertheless, Landau's presentation of the core of CM is clearer and more direct. For learning about the Lagrangian and Hamiltonian formalisms, rigid body rotation, small oscillations and canonical transformation, I found Landau to be the better book.
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49 of 54 people found the following review helpful:
5.0 out of 5 stars
Close to perfection., July 30, 1998
This review is from: Mechanics, Third Edition: Volume 1 (Course of Theoretical Physics) (Paperback)
This marvellous book of Landau, Lifshitz is the best adult presentation of "classical" classical mechanics, that is, leaving aside problems of stability, chaos, etc. With this proviso, the book is perfect. It is very short, not by omitting things, but by choosing (and rigidly adhering to it) a very sound philosophy: exploring the connection between symmetries and conservation laws. This explains why the dynamics is based on the action principle, which, as shown by Wigner, is the optimum language for expliciting the discoveries of Emmy Noether. The whole book follows this line, making the exposition very original and, at points, quite surprising (as when the mass is proved to be positive). In my opinion the climax of the book is the theory of the Hamilton-Jacobi equation, along the ideas of Jacobi. I know of no place where this is so admirably done. Simple and beautiful. After learning it, and the applications contained in the book, you can learn the miracles ! Landau and Lifshitz perform with this equation in all areas of physics, particularly in General Relativity.
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