Course of Theoretical Physics: Vol. 1 Mechanics 3rd Edition by L. D. Landau, ISBN-13: 978-0750628969

Description

Course of Theoretical Physics: Vol. 1 Mechanics 3rd Edition by L. D. Landau, ISBN-13: 978-0750628969

[PDF eBook eTextbook]

• Publisher: ‎ Butterworth-Heinemann; 3rd edition (January 15, 1976)
• Language: ‎ English
• 200 pages
• ISBN-10: ‎ 0750628960
• ISBN-13: ‎ 978-0750628969

Devoted 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.

Table of Contents:

Preface to the third English edition vii
L.D. Landau—a biography ix
I. THE EQUATIONS OF MOTION
§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
§6. Energy 13
§7. Momentum 15
§8. Centre of mass 16
§9. Angular momentum 18
§10. Mechanical similarity 22
III. INTEGRATION OF THE EQUATIONS OF MOTION
Motion in one dimension
Determination of the potential energy from the period of
oscillation
The reduced mass
Motion in a central field
Kepler’s problem
IV. COLLISIONS BETWEEN PARTICLES
§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
§21. Free oscillations in one dimension 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
§28. Anharmonic oscillations 84
§29. Resonance in non-linear oscillations 87
§30. Motion in a rapidly oscillating field 93
VI. MOTION OF A RIGID BODY
§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 asymmetrical top 116
§38. Rigid bodies in contact 122
§39. Motion in a non-inertial frame of reference 126
VII. THE CANONICAL EQUATIONS
§40. Hamilton’s equations 131
§41. TheRouthian 133
§42. Poisson brackets 135
§43. The action as a function of the 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 the variables 149
§49. Adiabatic invariants 154
§50. Canonical variables 157
§51. Accuracy of conservation of the adiabatic invariant 159
§52. Conditionally periodic motion 162

Lev Davidovich Landau was a Soviet-Azerbaijani physicist of Jewish descent who made fundamental contributions to many areas of theoretical physics.

His accomplishments include the independent co-discovery of the density matrix method in quantum mechanics (alongside John von Neumann), the quantum mechanical theory of diamagnetism, the theory of superfluidity, the theory of second-order phase transitions, the Ginzburg–Landau theory of superconductivity, the theory of Fermi liquids, the explanation of Landau damping in plasma physics, the Landau pole in quantum electrodynamics, the two-component theory of neutrinos, and Landau’s equations for S matrix singularities. He received the 1962 Nobel Prize in Physics for his development of a mathematical theory of superfluidity that accounts for the properties of liquid helium II at a temperature below 2.17 K (−270.98 °C).

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