INDEX 



363 



of system of particles, 220 ; of cen- 

 ter of gravity of any system, 224; 

 simple harmonic, 261; of particle 

 about a center of force, 26ft ; of par- 

 ticle under law of inverse square, 

 276. 



Neutral equilibrium, 182. 

 Newton's law, of elasticity, 245. 

 Newton's laws, of motion, 26. 

 Normal coordinates, 350. 



Orbit, general theory, 273 ; differential 

 equation of, 275. 



Orbit of a particle, law of direct dis- 

 tance, 269 ; law of inverse square of 

 distance, 276. 



Oscillations, of a pendulum, 298; 

 small, of a general dynamical sys- 

 tem, 348 ; forced, 363. 



Parallel forces, 96, 99. 



Parallelogram law, velocities, 9; ac- 

 celerations, 13 ; forces, 38 ; couples, 

 105 ; angular velocity, 286. 



Pendulum, simple, 259 ; seconds, 261 ; 

 cycloidal, 265 ; general motion of, 

 298. 



Period, of vibration, 261; of simple 

 harmonic motion, 265. 



Plane, composition of forces in one, 95 ; 

 orbit about a center of force confined 

 to one, 273. 



Planet, rotation of a, 309. 



Point of application, of a force, 60, 

 95. 



Potential energy, 163. 



Principal axes of inertia, 303. 



Principal coordinates, 350. 



Principle, of least action, 327 ; Ham- 

 ilton's, 323. 



Products of inertia, 302. 



Projectiles, 205 ; range on a horizontal 

 plane, 209 ; range on an inclined 

 plane, 209; envelope of paths with 

 given initial velocity, 211.. 



Pulleys, systems of, 157. 

 Pyramid, center of gravity of, 132. 



Quickest descent, line of, 193. 



Radius of gyration, 290. 



Range, of a projectile, 209. 



Reaction, 31 ; frictional, between 

 bodies at rest, 46; frictional, be- 

 tween bodies in motion, 200. 



Reference, frame of, 3, 33; motion of 

 frame of, 197. 



Relative motion, 4. 



Resonance, principle of, 354. 



Rest, 3. 



Restitution, impulse of, 240. 



Retardation, 12. 



Rigidity, 90. 



Rotation, axis of, 92 ; of earth, 198 ; 

 of a rigid body, kinetic energy of, 

 289 ; of a planet, 309. 



Sag, of a string, 85. 



Sector, of a circle, center of gravity of, 

 129; of a sphere, center of gravity 

 of, 134. 



Segment, of a circle, center of gravity 

 of, 128. 



Simple harmonic motion, 261. 



Spherical cap, center of gravity of, 130. 



Spinning top, motion of, 310. 



Stability and instability of equilib- 

 rium, 174, 351. 



Stars, double, orbits of, 280. 



Strings, tension of, 42 ; flexibility of, 

 43 ; extensibility of, 44 ; on surface, 

 74 ; sag of a stretched, 85 ; work of 

 stretching, 150. 



Suspension bridge, 78. 



System, of pulleys, 157 ; conservative, 

 of forces, 163. 



System of particles, statics of, 69 ; mo- 

 tion of, 220 ; kinetic energy of, 230. 



Tension, of a string, 42, 74. 

 Top, motion of, 310. 



