Mechanics

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Butterworth-Heinemann, 1976 - Science - 170 pages
11 Reviews
Devoted to the foundation of mechanics, namely classical Newtonian mechanics, the subject is based mainly on Galileo's principle of relativity and Hamilton's principle of least action. The exposition is simple and leads to the most complete direct means of solving problems in mechanics.

The final sections on adiabatic invariants have been revised and augmented. In addition a short biography of L D Landau has been inserted.

 

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One of the most significant moments in my Physics education came during my sophomore year in college. I decided to pick up a copy of "Mechanics" by Landau and Lifshitz that was on reserve in the library for the mechanics class that I was taking. This is the first volume in the internationally renowned series of textbooks on theoretical Physics, the series that has a reputation for its sparse and difficult writing style, as well as the undoubted difficulty and brilliance of the material presented. This is probably the reason why until that point I didn't even bother looking at these books, but for whatever reason that fateful night I decided to take a look at this particular volume. To my surprise, the book was actually pretty readable and the first few chapters revealed an entirely new way of looking at Physics. Until that point I was used to thinking about Physics as a set of laws and equations, relatively succinct but otherwise somewhat arbitrary and ad-hoc. Landau and Lifshitz's book started from a very different point; it gave some deep underlying principles as a starting point behind the development of physical laws and equations. Based on that I had a new and deeper appreciation of my chosen field of study, and I gained a whole new way of looking at the physical reality.
Granted, the book is really not a walk in the park. Many later chapters can be rather technically demanding, and a prior course on theoretical mechanics at college level is probably the minimal level of preparation that can get a reader through the whole text. There aren't all that many examples that are thoroughly worked out, but all of the problems are given (rather concise) solutions - you still need to fill in some of the more important steps on your own. Mechanics is not an area of active modern research, so this is not necessarily a book that will help one with their scientific careers. However, it provides a solid grounding in some of the most basic physical concepts, and the skills and techniques acquired here can be very important in other areas of Physics. All said, this is a classic textbook that anyone who is serious about a career in Physics would be well advised to go through.
 

Selected pages

Contents

THE EQUATIONS OF MOTION
1
2 The principle of least action
2
3 Galileos relativity principle
4
4 The Lagrangian for a free particle
6
5 The Lagrangian for a system of particles
8
CONSERVATION LAWS
13
7 Momentum
15
8 Centre of mass
16
28 Anharmonic oscillations
84
29 Resonance in nonlinear oscillations
87
30 Motion in a rapidly oscillating field
93
MOTION OF A RIGID BODY
96
32 The inertia tensor
98
33 Angular momentum of a rigid body
105
34 The equations of motion of a rigid body
107
35 Eulerian angles
110

9 Angular momentum
18
10 Mechanical similarity
22
INTEGRATION OF THE EQUATIONS OF MOTION
25
12 Determination of the potential energy from the period of oscillation
27
13 The reduced mass
29
14 Motion in a central field
30
15 Keplers problem
35
COLLISIONS BETWEEN PARTICLES
41
17 Elastic Collisions
44
18 Scattering
48
19 Rutherfords formula
53
20 Smallangle scattering
55
SMALL OSCILLATIONS
58
22 Forced oscillations
61
23 Oscillations of systems with more than one degree of freedom
65
24 Vibrations of molecules
70
25 Damped oscillations
74
26 Forced oscillations under friction
77
27 Parametric resonance
80
36 Eulers equations
114
37 The asymmetrical top
116
38 Rigid bodies in contact
122
39 Motion in a noninertial frame of reference
126
THE CANONICAL EQUATIONS
131
41 The Routhian
133
42 Poisson brackets
135
43 The action as a function of the coordinates
138
44 Maupertuis principle
140
45 Canonical transformations
143
46 Liouvilles theorem
146
47 The HamiltonJacob equation
147
48 Separation of the variable
149
49 Adiabatic invariants
154
50 Canonical variables
157
51 Accuracy of conservation of the adiabatic invariant
159
52 Conditionally periodic motion
162
Index
168
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About the author (1976)

Lev Davidovich Landau was born on January 22, 1908 in Baku, U.S.S.R (now Azerbaijan). A brilliant student, he had finished secondary school by the age of 13. He enrolled in the University of Baku a year later, in 1922, and later transferred to the University of Leningrad, from which he graduated with a degree in physics. Landau did graduate work in physics at Leningrad's Physiotechnical Institute, at Cambridge University in England, and at the Institute of Theoretical Physics in Denmark, where he met physicist Neils Bohr, whose work he greatly admired. Landau worked in the Soviet Union's nuclear weapons program during World War II, and then began a teaching career. Considered to be the founder of a whole school of Soviet theoretical physicists, Landau was honored with numerous awards, including the Lenin Prize, the Max Planck Medal, the Fritz London Prize, and, most notably, the 1962 Nobel Prize for Physics, which honored his pioneering work in the field of low-temperature physics and condensed matter, particularly liquid helium. Unfortunately, Landau's wife and son had to accept the Nobel Prize for him; Landau had been seriously injured in a car crash several months earlier and never completely recovered. He was unable to work again, and spent the remainder of his years, until his death in 1968, battling health problems resulting from the accident. Landau's most notable written work is his Course of Theoretical Physics, an eight-volume set of texts covering the complete range of theoretical physics. Like several other of Landau's books, it was written with Evgeny Lifshitz, a favorite student, because Landau himself strongly disliked writing. Some other works include What is Relativity?, Theory of Elasticity, and Physics for Everyone.

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