MechanicsDevoted 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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Review: Course of Theoretical Physics: Vol. 1, Mechanics
User Review  Rich Bergmann  GoodreadsTHE definitive treatment of Mechanics by one of the best mathematical physicists that ever lived. Read full review
Review: Course of Theoretical Physics: Vol. 1, Mechanics
User Review  GoodreadsTHE definitive treatment of Mechanics by one of the best mathematical physicists that ever lived. Read full review
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 
168  
Common terms and phrases
adiabatic invariant amplitude angular momentum angular velocity arbitrary constants axes of inertia axis called canonical transformation centre of mass closed system coordinates q coefficients collision components consider corresponding degrees of freedom depends Determine effective crosssection equations of motion expressed in terms external field external force finite forced oscillations formula frame of reference frequency friction function generalised coordinates given gives HamiltonJacobi equation Hamilton's equations Hamiltonian Hence homogeneous homogeneous function inertial frame interaction kinetic energy Lagrange's equations Lagrangian Landau law of conservation least action linear mechanical system molecule momenta obtain parameter path period perpendicular plane Poisson bracket position potential energy principal axes principle of least PROBLEMS PROBLEM properties quantities radius vector resonance respect result righthand side rigid body rotation scattering small oscillations SOLUTION substituting symmetrical system of coordinates theoretical physics theory tion total time derivative variables vertical zero