CONTENTS. XI 



CHAPTER XI. 



FREEDOM OF THE SECOND ORDER. 

 H 



oo 



116. The Screw System of the Second Order .... 



117. Applications of Screw Co-ordinates ..... 



118. Relation between Two Cylindroids 



119. Co-ordinates of Three Screws on a Cylindroid . 



120. Screws on One Line ........ 



121. Displacement of a Point 



122. Properties of the Pitch Conic 



123. Equilibrium of a Body with Freedom of the Second Order 



124. Particular Cases ..... ... 



125. The Impulsive Cylindroid and the Instantaneous Cylindroid 



126. Reaction of Constraints 



127. Principal Screws of Inertia ....... 



128. The Ellipse of Inertia . . . . . . 



129. The Ellipse of the Potential 



130. Harmonic Screws ......... 



131. Exceptional Case 



132. Reaction of Constraints. ..... 



CHAPTER XTI. 



PLANE REPRESENTATION OF DYNAMICAL PROBLEMS CONCERNING A BODY 

 WITH Two DEGREES OF FREEDOM. 



133. The Kinetic Energy 120 



134. Body with Two Degrees of Freedom 120 



135. Conjugate Screws of Inertia 124 



136. Impulsive Screws and Instantaneous Screws 125 



137. Two Homographic Systems .......... 126 



138. The Homographic Axis 127 



139. Determination of the Homographic Axis . . . . . . . 128 



140. Construction for Instantaneous Screws . . . . . . 128 



141. Twist Velocity acquired by an Impulse ....... 129 



142. Another Construction for the Twist Velocity 129 



143. Twist Velocities on the Principal Screws 131 



144. Another Investigation of the Twist Velocity acquired by an Impulse . . 131 



145. A Special Case 133 



146. Another Construction for the Twist Velocity acquired by an Impulse . 134 



147. Constrained Motion 136 



148. Energy acquired by an Impulse 137 



149. Euler s Theorem 138 



150. To determine a Screw that will acquire a given Twist Velocity under 



a given Impulse 138 



151. Principal Screws of the Potential 140 



