viii CONTENTS 



PAGK 

 CHAPTER VIII. MOTION OF A PARTICLE UNDER CONSTANT FORCES 188 



Body falling under gravity. Motion on an inclined plane. At- 

 wood's machine. Motion referred to a moving frame of reference. 

 Frictional reactions between moving bodies. Flight of projectiles. 



CHAPTER IX. MOTION OF SYSTEMS OF PARTICLES 220 



Equations of motion. Conservation of momentum. Motion of 

 center of gravity. Kinetic energy. Impulsive forces. Elasticity. 



CHAPTER X. MOTION OF A PARTICLE UNDER A VARIABLE FORCE 254 



Equations of motion. The simple pendulum. Simple harmonic 

 motion. The cycloidal pendulum. Motion of a particle about a 

 center of force, force proportional to the distance. General theory 

 of motion about a center of force. The law of the inverse square. 



CHAPTER XI. MOTION OF RIGID BODIES 286 



Angular velocity. Kinetic energy. Radii of gyration. Moment of 

 momentum. General theory of moments of inertia. General equa- 

 tions of motion of a rigid body. Euler's equations. Rotation of a 

 planet. Motion of a top. 



CHAPTER XII. GENERALIZED COORDINATES 320 



Hamilton's principle. Principle of least action. Lagrange's equa- 

 tions. Small oscillations. Stability and instability of equilibrium. 

 Forced oscillations. The canonical equations. 



INDEX 361 



