Mathematical Methods of Classical Mechanics

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Springer Science & Business Media, May 16, 1989 - Mathematics - 508 pages
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In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
  

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Advanced classical mechanics book. Maybe you don't feel very useful at first, but you WILL definitely find this helpful for you to understand classical mechanics deeply, e.g. what exactly is Poisson bracket. This is absolutely a fantastic book for physicists!

Contents

III
1
IV
3
V
4
VI
11
VII
15
VIII
22
IX
28
X
30
XL
181
XLI
188
XLII
201
XLIII
204
XLIV
208
XLV
214
XLVI
219
XLVII
225

XI
33
XII
42
XIII
44
XIV
50
XV
53
XVI
55
XVII
59
XVIII
61
XIX
65
XX
68
XXI
75
XXII
77
XXIII
83
XXIV
88
XXV
91
XXVI
98
XXVII
103
XXVIII
110
XXIX
113
XXX
123
XXXI
129
XXXII
133
XXXIII
142
XXXIV
148
XXXV
154
XXXVI
161
XXXVII
163
XXXVIII
170
XXXIX
174
XLVIII
229
XLIX
233
L
240
LI
248
LII
258
LIII
266
LIV
271
LV
279
LVI
285
LVII
291
LVIII
301
LIX
318
LX
343
LXI
349
LXII
371
LXIII
381
LXIV
385
LXV
399
LXVI
416
LXVII
425
LXVIII
438
LXIX
446
LXX
453
LXXI
456
LXXII
469
LXXIII
480
LXXIV
511
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About the author (1989)

Arnol'd, Steklov Mathematical Institute

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