CONTENTS. 



IX 



CHAPTER VII. 

 Dynamics of Rotating Bodies. 



Page 



250 



Art. 



80. Dynamics of Body moving 

 about a Fixed Axis . . . 



81. Motion of a Rigid Body 

 about a Fixed Point. Kine- 

 matics 252 



82. Dynamics. Motion under no 

 Forces 256 



84. Euler's Dynamical Equa- 

 tions .... 260 



85. Poinsot's Discussion of the 

 Motion 261 



86. Stability of Axes .... 264 



87. Projections of the Polhode . 264 



88. Invariable Line 265 



89. Symmetrical Top. Constrained 

 Motion 271 



90. Heavy Symmetrical Top . . 274 



91. Top Equations deduced by 

 Lagrange's Method .... 277 



92. Nature of the Motion ... 279 



93. Precession and Nutation . 283 



Art. p a g e 



94. Small Oscillations about the 

 Vertical 288 



95. Top Equations deduced by 

 Jacobi's Method . . . . 297 



96. Rotation of the Earth. Pre- 

 cession and Nutation. . . 298 



97. Top on smooth Table . . 302 



98. Effect of Friction. Rising 



of Top 303 



99. Motion of a Billiard Ball . 304 



100. Pure Rolling 307 



101. Lagrange's Equations ap- 

 plied to Rolling. Noninte- 

 grable Constraints . . . 313 



102. Moving Axes . . . . . 316 



103. Rotating Axes. Theorem of 

 Coriolis 317 



104. Motion relatively of the Earth 320- 



105. Motion of a Spherical Pen- 

 dulum 323 



106. Foucault's Gyroscope . . 324 



PART III. 



THEORY OP THE POTENTIAL, DYNAMICS OF 

 DEFORMABLE BODIES. 



CHAPTER VIII. 

 Newtonian Potential Function. 



107. Point -Function 329 



108. Level Surface of Scalar 

 Point -Function . . . .. . 329 



109. Coordinates 330 



110. Differential Parameter . . 330 



111. Polar Coordinates .... 334 



112. Cylindrical, or Semi-polar 

 Coordinates 335 



113. Ellipsoidal Coordinates . . 335 



114. Infinitesimal Arc, Area and 

 Volume ., 338 



115. Connectivity of Space. 

 Green's Theorem .... 339 



116. Second Differential Para- 

 meter 344 



117. Divergence. Solenoidal Vec- 

 tors 347 



118. Reciprocal Distance. Gauss's 

 Theorem . . . . . . . 350 



WEBSTER, Dynamics. 



119. Definition and fundamental 

 Properties of Potential . . 352 



120. Potential of Continuous Dis- 

 tribution 353 



121. Derivatives ...... 355 



122. Points in the Attracting Mass. 357 



123. Poisson's Equation . . . 359 



124. Characteristics of Potential 

 Function 362 



125. Examples. Potential of a 

 homogeneous Sphere . . . 363 



126. Disc, Cylinder, Cone . . 366 



127. Surface Distributions . . 367 



128. Green's Formulae .... 370 



129. Equipotential Layers . . . 372 



130. Gauss's Mean Theorem . . 374 



131. Potential completely deter- 

 mined by its characteristic 

 Properties ...... 375 



a* 



