A Treatise on the Theory of Screws
Forfatter: Sir Robert Stawell Ball
År: 1900
Forlag: The University Press
Sted: Cambride
Sider: 544
UDK: 531.1
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CONTENTS,
XI
CHAPTER XI .
Freedom of the Second Order.
PAGE
116. The Screw System of the Second Order.......................................107
117. Applications of Screw Co-ordinates.........................................107
118. Relation between Two Cylindroids...........................................108
119. Co-ordinates of Three Screws on a Cylindroid...............................108
120. Screws on One Line . , 109
121. Displacement of a Point....................................................110
122. Properties of the Pitch Conic.............................. . . . no
123. Equilibrium of a Body with Freedom of the Second Order . . . Ill
124. Particular Cases......................................................... 112
125. The Impulsive Cylindroid and the Instantaneous Cylindroid . , . 112
126. lieaction of Constraints...................................................114
127. Principal Screws of Inertia................................................114
128. The Ellipse of Inertia.....................................................114
129. The Ellipse of the Potential...............................................116
130. Harmonic Screws............................................................118
131. Exceptional Case...........................................................118
132. Reaction of Constraints. . . . . . . . . , . 119
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