FOREWORD TO SOMMERFELD'S COURSE BY P. P. EWALD
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?
CEAPTER Ⅱ.  MECHANICS OF SYSTEMS, PRINCIPLE OF VIRTUAL WORK, ANDD'ALEMBERT'S PRINCIPLE
  7.Degrees of Freedom and Virtual Displacements of a Mechanical Syatem;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
    (6)General Rule on the Number of Integrations Feasible in a Closed
    (5)Mass Balancing of Marine Engines Syetem
  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 Pendulurm
  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 and Euler'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, 159—
      (c)Trajectories with " English " Under Horizontal Impact, 160—
      (d)Parabolic Path Due to Shot with Vertical Component, 160
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 Heevy 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 Geodesics
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-oylinder 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 unsyrmmetrical bodyabout 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
  FOB 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
  FOB 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 PROBLEMS
INDEX