The Problem of Columbus. 



459 



CG be C, and about any perpendicular to OG through G be A. 

 Let Z.ZCG=# and the angular velocity of the plane ZOX 

 about OZ be ^r. Let R be the normal reaction at and 

 F l5 F 2 the components of the friction along OX, OY. Take 



GA the perpendicular to GC in the plane ZCG, GB the per- 

 pendicular to this plane, and GC / the axis of the body as 

 principal axes. They will coincide in direction with OX, 

 OY, OZ when = 0. Let the spins of the body round them 

 be <»!, &> 2 , ft>s, and the spins of the axes round their instan- 

 taneous positions be l5 6 2 , 3 . Also let the velocities of G 

 parallel to OX, OY, OZ be u, v, iv. 

 3. Then we have clearly 



&>! = 

 ft>2 = 

 *1 = 



e.,= 



— yfr sin 6 



e I 



ty cos 



(1) 



