1 Introduction: Newtonian Mechanics ............................ 1
2 Generalized Coordinates and Lagrange's Equations ............. 7
3 The Hamilton and Weiss Variational Principles and the
Hamilton Equations of Motion ................................ 13
4 The Relation Between the Lagrangian and the Hamiltonian
Descriptions ................................................ 23
5 Invariance Properties of the Lagrangian & Hamiltonian
Descriptions, Poisson and Lagrange Brackets, and Canonical
Transformations ............................................. 31
6 Group Properties and Methods of Constructing Canonical
Transformations ............................................. 45
7 Invariant Measures in Phase Space and Various Forms of
Development in Time ......................................... 65
8 Theory of Systems with Constraints .......................... 77
9 The Generalized Poisson Bracket and Its Applications ....... 107
10 Dynamical Systems with Infinitely Many Degrees of Freedom
and Theory of Fields ....................................... 135
11 Linear and Angular Momentum Dynamical Variables and Their
Significance ............................................... 151
12 Sets, Topological Spaces, Groups ........................... 163
13 Lie Groups and Lie Algebras ................................ 177
14 Realizations of Lie Groups and Lie Algebras ................ 205
15 Some Important Lie Groups and Their Lie Algebras ........... 231
16 Relativistic Symmetry in the Hamiltonian Formalism ......... 277
17 The Three-Dimensional Rotation Group ....................... 299
18 The Three-Dimensional Euclidean Group ...................... 351
19 The Galilei Group .......................................... 363
20 The Poincare Group ......................................... 427
21 Manifest Covariance in Hamiltonian Mechanics ............... 495
22 Relativistic Action-at-a-Distance Theories ................. 545
23 Conclusion ................................................. 575
Index ......................................................... 581
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