Mechanics: Volume 1Devoted 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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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 | |
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Common terms and phrases
adiabatic invariant amplitude angle angular momentum angular velocity axes of inertia axes x1 axis canonical transformation centre of mass co-ordinates q coefficients collision components corresponding degrees of freedom depends Determine effective cross-section equations of motion expressed in terms external field external force forced oscillations formula frame of reference frequency friction function generalised co-ordinates given gives Hamilton-Jacobi equation Hamilton's equations Hamiltonian Hence homogeneous homogeneous function I₁ inertial frame interaction kinetic energy Lagrange's equations Lagrangian Landau law of conservation least action linear M₁ mechanical system molecule momenta obtain parameter path period perpendicular plane Poisson bracket position potential energy principal axes PROBLEMS PROBLEM quantities radius vector resonance respect result right-hand side rigid body rotation scattering small oscillations SOLUTION substituting symmetrical system of co-ordinates theoretical physics theory tion total time derivative variables vertical x-axis zero