Mechanics

Foreword to Sommerfelds's Course Preface to the First Edition Introduction Chapter I. Mechanics of a Particle 1. Newton's Axioms 2. Space, Time and Reference Systems 3. Rectilinear Motion of a Mass Point Examples: (1) Free Fall Near Earth's Surface (Falling Stone) (2) Free Fall From a Great Distance (Meteor) (3) Free Fall in Air (4) Harmonic Oscillations (5) Collision of Two Particles 4. Variable Masses 5. Kinematics and Statics of a Single Mass Point in a Plane and in Space (1) Plane Kinematics (2) The Concept of Moment in Plane Statics and Kinematics (3) Kinematics in Space (4) Statics in Space; Moment of Force About a Point and About an Axis 6. Dynamics (Kinetics) of the Freely Moving Mass Point; Kepler Problem; Concept of Potential Energy (1) Kepler Problem with Fixed Sun (2) Kepler Problem Including Motion of the Sun (3) When Does a Force Field Have a Potential? Chapter II. Mechanics of Systems, Principle Of Virtual Work, and d'alembert's Principle 7. Degrees of Freedom and Virtual Displacements of a Mechanical System; Holonomic and Non-holonomic Constraints 8. The Principle of Virtual Work 9. Illustrations of the Principle of Virtual Work (1) The Lever (2) Inverse of the Lever: Cyclist, Bridge (3) The Block and Tackle (4) The Drive Mechanism of a Piston Engine (5) Moment of a Force About an Axis and Work in a Virtual Rotation 10. D'Alembert's Principle; Introduction of Inertial Forces 11. Application of d'Alembert's Principle to the Simplest Problems (1) Rotation of a Rigid Body About a Fixed Axis (2) Coupling of Rotational and Translational Motion (3) Sphere Rolling on Inclined Plane (4) Mass Guided Along Prescribed Trajectory 12. Lagrange's Equations of the First Kind 13. Equations of Momentum and of Angular Momentum (1) Equation of Momentum (2) Equation of Angular Momentum (3) Proof Using the Coordinate Method (4) Examples (5) Mass Balancing of Marine Engines (6) General Rule on the Number of Integrations Feasible in a Closed System 14. The Laws of Friction (1) Static Friction (2) Sliding Friction Chapter III. Oscillation Problems 15. The Simple Pendulum 16. The Compound Pendulum Supplement: A Rule Concerning Moments of Inertia 17. The Cycloidal Pendulum 18. The Spherical Pendulum 19. Various Types of Oscillations. Free and Forced, Damp and Undamped Oscillations 20. Sympathetic Oscillations 21. The Double Pendulum Chapter IV. The Rigid Body 22. Kinematics of Rigid Bodies 23. Statics of Rigid Bodies (1) The Conditions of Equilibrium (2) Equipollence ; the Reduction of Force Systems (3) Change of Reference Point (4) Comparison of Kinematics and Statics Supplement: Wrenches and Screw Displacements 24. Linear and Angular Momentum of a Rigid Body. Their Connection with Linear and Angular Velocity 25. Dynamics of a Rigid Body. Survey of its Forms of Motion (1) The Spherical Top Under No Forces (2) The Symmetrical Top Under No Forces (3) The Unsymmetrical Top Under No Forces (4) The Heavy Symmetrical Top (5) The Heavy Unsymmetrical Top 26. Euler's Equations. Quantitative Treatment of the Top Under No Forces (1) Euler's Equations of Motion (2) Regular Precession of the Symmetrical Top Under No Forces andEuler's Theory of Polar Fluctuations (3) Motion of an Unsymmetrical Top Under No Forces. Examination of its Permanent Rotations as to Stability 27. Demonstration Experiments Illustrating the Theory of the Spinning Top; Practical Applications (1) The Gyrostabilizer and Related Topics (2) The Gyrocompass (3) Gyroscopic Effects in Railroad Wheels and Bicycles Supplement: The Mechanics of Billiards (a) High and Low Shots, 158—(b) Follow Shots and Draw Shots, (c) Trajectories with "English" Under Horizontal Impact, (d) Parabolic Path Due to Shot with Vertical Component, Chapter V. Relative Motion 28. Derivation of the Coriolis Force in a Special Case 29. The General Differential Equations of Relative Motion 30. Free Fall on the Rotating Earth; Nature of the Gyroscopic Terms 31. Foucault's Pendulum 32. Lagrange's Case of the Three-Body Problem Chapter VI. Integral Variational Principles Of Mechanics and Lagrange's Equations For Generalized Coordinates 33. Hamilton's Principle 34. Lagrange's Equations for Generalized Coordinates 35. Examples Illustrating the Use of Lagrange's Equations (1) The Cycloidal Pendulum (2) The Spherical Pendulum (3) The Double Pendulum (4) The Heavy Symmetrical Top 36. An Alternate Derivation of Lagrange's Equations 37. The Principle of Least Action Chapter VII. Differential Variational Principles Of Mechanics 38. Gauss' Principle of Least Constraint 39. Hertz's Principle of Least Curvature 40. A Digression on Geodesies Chapter VIII. The Theory Of Hamilton 41. Hamilton's Equations (1) Derivation of Hamilton's Equations from Lagrange's Equations (2) Derivation of Hamilton's Equations from Hamilton's Principle 42. Routh's Equations and Cyclic Systems 43. The Differential Equations for Non-Holonomic Velocity Parameters 44. The Hamilton-Jacobi Equation (1) Conservative Systems (2) Dissipative Systems 45. Jacobi's Rule on the Integration of the Hamilton-Jacobi Equation 46. Classical and Quantum-Theoretical Treatment of the Kepler Problem Problems For Chapter I I.1, I.2, I.3. Elastic collision I.4. Inelastic collision between an electron and an atom I.5. Rocket to the moon I.6. Water drop falling through saturated atmosphere I.7. Falling chain I.8. Falling rope I.9. Acceleration of moon due to earth's attraction I.10. The torque as vector quantity I.11. The hodograph of planetary motion I.12. Parallel beam of electrons passing through the field of an ion. Envelope of the trajectories I.13. Elliptical trajectory under the influence of a central force directly proportional to the distance I.14. Nuclear disintegration of lithium I.15. Central collisions between neutrons and atomic nuclei; effect of a block of paraffin I.16. Kepler's equation For Chapter II II.1. Non-holonomic conditions of a rolling wheel II.2. Approximate design of a flywheel for a double-acting one-cylinder steam engine II.3. Centrifugal force under increased rotation of the earth II.4. Poggendorff's experiment II.5. Accelerated inclined plane II.6. Products of inertia for the uniform rotation of an unsymmetrical body about an axis II.7. Theory of the Yo-yo II.8. Particle moving on the surface of a sphere For Chapter III III.1. Spherical pendulum under infinitesimal oscillations III.2. Position of the resonance peak of forced damped oscillations III.3. The galvanometer III.4. Pendulum under forced motion of its point of suspension III.5. Practical arrangement of coupled pendulums III.6. The oscillation quencher For Chapter IV IV.1. Moments of inertia of a plane mass distribution IV.2. Rotation of the top about its principal axes IV.3. High and low shots in a billiard game. Follow shot and draw shot IV.4. Parabolic motion of a billiard ball For Chapter V V.1. Relative motion in a plane V.2. Motion of a particle on a rotating straight line V.3. The sleigh as the simplest example of a non-holonomic system For Chapter VI VI.1. Example illustrating Hamilton's principle VI.2. Relative motion in a plane and motion on a rotating straight line VI.3. Free fall on the rotating earth and Foucault's pendulum VI.4. "Wobbling" of a cylinder rolling on a plane support VI.5. Differential of an automobile Hints for Solving the ProblemsIndex