A Treatise on the Theory of Screws

CONTENTS. xiii §§ PAGE 189. Relation between the Impulsive Screw and the Instantaneous Screw . 189 190. Kinetic Energy acquired by an Impulse.......................................189 191. Reaction of the Constraints.................................................191 192. Impulsive Screw is Indeterminate............................................191 193. Quadric of the Potential....................................................192 194. The Principal Screws of the Potential.......................................192 195. Wrench evoked by Displacement...............................................193 196. Harmonic Screws.............................................................193 197. Oscillations of a Rigid Body about a Fixed Point............................194 CHAPTER XV . The Plane Representation of Freedom of the Third Order. 198. A Fundamental Consideration.................................................197 199. The Plane Representation....................................................198 200. The Cylindroid..............................................................199 201. The Screws of the Three-System..............................................200 202. Imaginary Screws............................................................201 203. Relation of the Four Planes to the Quadrics.................................202 204. The Pitch Conics............................................................204 205. The Angle between Two Screws................................................204 206. Screws at Right Angles......................................................206 207. Reciprocal Screws ............ 206 208. The Principal Screws of the System..........................................207 209. Expression for the Pitch....................................................208 210. Intersecting Screws in a Three-System.......................................212 211. Application to Dynamics.....................................................214 CHAPTER XVI . Freedom of the Fourth Order. 212. Screw System of the Fourth Order.........................................218 213. Equilibrium with Freedom of the Fourth Order.............................219 214. Screws of Stationary Pitch...............................................221 215. Applications of the Two-System ......... 224 216. Application to the Three-System..........................................226 217. Principal Pitches of the Reciprocal Cylindroid...........................227 218. Equations to the Screw in a Four-System..................................229 219. Impulsive Screws and Instantaneous Screws................................229 220. Principal Screws of Inertia in the Four-System...........................230 221. Application of Euler’s Theorem...........................................231 222. General Remarks.........................................................2,32 223. Quadratic »-systems......................................................233 224. Properties of a Quadratic Two-System.....................................234 225. The Quadratic Systems of Higher Orders...................................235