Mechanics

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.

Contenu

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 …