《MECHANICS THIRD EDITION COURSE OF THEORETICAL PHYSICS VOLUME 1》

Ⅰ.THE EQUATIONS OF MOTION1

1.Generalised co-ordinates1

2.The principle of least action2

3.Galileo’s relativity principle4

4.The Lagrangian for a free particle6

5.The Lagrangian for a system of particles8

Ⅱ.CONSERVATION LAWS13

6.Energy13

7.Momentum15

8.Centre of mass16

9.Angular momentum18

10.Mechanical similarity22

Ⅲ.INTEGRATION OF THE EQUATIONS OF MOTION25

11.Motion in one dimension25

12.Determination of the potential energy from the period of oscillation27

13.The reduced mass29

14.Motion in a central field30

15.Kepler’s problem35

Ⅳ.COLLISIONS BETWEEN PARTICLES41

16.Disintegration of particles41

17.Elastic collisions44

18.Scattering48

19.Rutherford’s formula53

20.Small-angle scattering55

Ⅴ.SMALL OSCILLATIONS58

21.Free oscillations in one dimension58

22.Forced oscillations61

23.Oscillations of systems with more than one degree of freedom65

24.Vibrations of molecules70

25.Damped oscillations74

26.Forced oscillations under friction77

27.Parametric resonance80

28.Anharmonic oscillations84

29.Resonance in non-linear oscillations87

30.Motion in a rapidly oscillating field93

Ⅵ.MOTION OF A RIGID BODY96

31.Angular velocity96

32.The inertia tensor98

33.Angular momentum of a rigid body105

34.The equations of motion of a rigid body107

35.Eulerian angles110

36.Euler’s equations114

37.The asymmetrical top116

38.Rigid bodies in contact122

39.Motion in a non-inertial frame of reference126

Ⅶ.THE CANONICAL EQUATIONS131

40.Hamilton’s equations131

41.The Routhian133

42.Poisson brackets135

43.The action as a function of the co-ordinates138

44.Maupertuis’ principle140

45.Canonical transformations143

46.Liouville’s theorem146

47.The Hamilton-Jacobi equation147

48.Separation of the variables149

49.Adiabatic invariants154

50.Canonical variables157

51.Accuracy of conservation of the adiabatic invariant159

52.Conditionally periodic motion162

Index167