Sommerfeld Mechanics

Lectures on Theoretical Physics
1. Auflage 2013
ISBN: 978-1-4832-2028-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 304 Seiten, Web PDF

Mechanics: Lectures on Theoretical Physics, Volume I covers a general course on theoretical physics. The book discusses the mechanics of a particle; the mechanics of systems; the principle of virtual work; and d'alembert's principle. The text also describes oscillation problems; the kinematics, statics, and dynamics of a rigid body; the theory of relative motion; and the integral variational principles of mechanics. Lagrange's equations for generalized coordinates and the theory of Hamilton are also considered. Physicists, mathematicians, and students taking Physics courses will find the book invaluable.

Autoren/Hrsg.

Sommerfeld, Arnold

Inhaltsverzeichnis

1;Front Cover;1
2;Mechanics: Lectures on Theoretical Physics;4
3;Copyright Page;5
4;Table of Contents;12
5;FOREWORD TO SOMMERFELDES COURSE;6
6;PREFACE TO THE FIRST EDITION, SEPTEMBER 1942;10
7;INTRODUCTION;16
8;CHAPTER I. MECHANICS OF A PARTICLE;18
8.1;1. Newton's Axioms;18
8.2;2. Space, Time and Reference Systems;24
8.3;3. Rectilinear Motion of a Mass Point;31
8.4;4. Variable Masses;43
8.5;5. Kinematics and Statics of a Single Mass Point in a Plane and in Space;47
8.6;6. Dynamics (Kinetics) of the Freely Moving Mass Point; Kepler Problem; Concept of Potential Energy;53
9;CHAPTER II. MECHANICS OF SYSTEMS, PRINCIPLE OF VIRTUAL WORK, AND D'ALEMBERT'S PRINCIPLE;63
9.1;7. Degrees of Freedom and Virtual Displacements of a Mechanical System; Holonomic and Non-holonomic Constraints;63
9.2;8. The Principle of Virtual Work;66
9.3;9. Illustrations of the Principle of Virtual Work;69
9.4;10. D'Alembert's Principle; Introduction of Inertial Forces;74
9.5;11. Application of d'Alembert's Principle to the Simplest Problems;77
9.6;12. Lagrange's Equations of the First Kind;81
9.7;13. Equations of Momentum and of Angular Momentum;84
9.8;14. The Laws of Friction;96
10;CHAPTER III. OSCILLATION PROBLEMS;102
10.1;15. The Simple Pendulum;102
10.2;16. The Compound Pendulum;106
10.3;17. The Cycloidal Pendulum;109
10.4;18. The Spherical Pendulum;111
10.5;19. Various Types of Oscillations. Free and Forced, Damp and Undamped Oscillations;115
10.6;20. Sympathetic Oscillations;121
10.7;21. The Double Pendulum;126
11;CHAPTER IV. THE RIGID BODY;133
11.1;22. Kinematics of Rigid Bodies;133
11.2;23. Statics of Rigid Bodies;140
11.3;24. Linear and Angular Momentum of a Rigid Body. Their Connection with Linear and Angular Velocity;145
11.4;25. Dynamics of a Rigid Body. Survey of its Forms of Motion;148
11.5;26. Euler's Equations. Quantitative Treatment of the Top Under No Forces;154
11.6;27. Demonstration Experiments Illustrating the Theory of the Spinning Top; Practical Applications;165
12;CHAPTER V. RELATIVE MOTION;177
12.1;28. Derivation of the Coriolis Force in a Special Case;177
12.2;29. The General Differential Equations of Relative Motion;180
12.3;30. Free Fall on the Rotating Earth; Nature of the Gyroscopic Terms;182
12.4;31. Foucault's Pendulum;186
12.5;32. Lagrange's Case of the Three-Body Problem;189
13;CHAPTER VI. INTEGRAL VARIATIONAL PRINCIPLES OF MECHANICS AND LAGRANGE'S EQUATIONS FOR GENERALIZED COORDINATES;196
13.1;33. Hamilton's Principle;196
13.2;34. Lagrange's Equations for Generalized Coordinates;200
13.3;35. Examples Illustrating the Use of Lagrange's Equations;207
13.4;36. An Alternate Derivation of Lagrange's Equations;215
13.5;37. The Principle of Least Action;219
14;CHAPTER VII. DIFFERENTIAL VARIATIONAL PRINCIPLES OF MECHANICS;225
14.1;38. Gauss' Principle of Least Constraint;225
14.2;39. Hertz's Principle of Least Curvature;227
14.3;40. A Digression on Geodesics;229
15;CHAPTER VIII. THE THEORY OF HAMILTON;232
15.1;41. Hamilton's Equations;232
15.2;42. Routh's Equations and Cyclic Systems;237
15.3;43. The Differential Equations for Non-Holonomic Velocity Parameters;241
15.4;44. The Hamilton-Jacobi Equation;244
15.5;45. Jacobi's Rule on the Integration of the Hamilton-Jacobi Equation;248
15.6;46. Classical and Quantum-Theoretical Treatment of the Kepler Problem;250
16;PROBLEMS;255
16.1;FOR CHAPTER I;255
16.2;FOR CHAPTER II;259
16.3;FOR CHAPTER III;262
16.4;FOR CHAPTER IV;265
16.5;FOR CHAPTER V;266
16.6;FOR CHAPTER VI;267
17;HINTS FOR SOLVING THE PROBLEMS;271
18;INDEX;298