Ⅰ．THE EQUATIONS OF MOTION 1
1．Generalised co-ordinates 1
2．The principle of least action 2
3．Galileo's relativity principle 4
4．The Lagrangian for a free particle 6
5．The Lagrangian for a system of particles 8
Ⅱ．CONSERVATION LAWS 13
6．Energy 13
7．Momentum 15
8．Centre of mass 16
9．Angular momentum 18
0．Mechanical similarity 22
Ⅲ．INTEGRATION OF THE EQUATIONS OF MOTION 22
11．Motion in one dimension 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．Kepler's problem 35
Ⅳ．COLLISIONS BETWEEN PARTICLES 41
16．Disintegration of particles 41
17．Elastic collisions 44
18．Scattering 48
19．Rutherford's formula 53
20．Small-angle scattering 55
Ⅴ．SMALL OSCILLATIONS 58
21．Free oscillations in one dimension 58
22．Foreed oscillations 61
23．Oscillations of systems with more than one degree offreedom 65
24．Vibrations of molecules 70
25．Damped oscillations 74
26．Forced oscillations under friction 77
27．Parametric resonance 80
28．Anharmonic oscillations 84
29．Resonance in non-linear oscillations 87
30．Motionin arapidly oscillatingfield 93
Ⅵ．MOTION OF A RIGID BODY 96
31．Angular velocity 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
36．Euler's equations 114
37．The asymmctrical top 116
38．Rigidbodies in contact 122
39．Motion in a non-inertial frame of reference 126
Ⅶ．THE CANONICAL EQUATIONS 131
40．Hamilton's equations 131
41．The Routhian 133
42．Poisson brackets 135
43．The action as a function ofthe co-ordinates 138
44．Maupertuis' principle 140
45．Canonical transformations 143
46．Liouville's theorem 146
47．The Hamilton-Jacobi equation 147
48．Separation of thevariables 149
49．Adiabatic invariants 154
50．Canonical variables 157
51．Accuracy of conservation of the adiabatic invariant 159
52．Conditionally periodic motion 162
Index 167