310 MOTION OF RIGID BODIES 



and we see that the axis of rotation describes a cone in the solid, 



. , 27T 27T B 



with period - or 



K &L -D A. 



If B is very nearly equal to A, the period may be very great, 

 and the motion consequently very slow. This happens in the case 

 of the earth : the motion of the axis of rotation gives rise to the 

 phenomenon known as the variation of latitude, of which . the 



period is about 428 days. Since a period - represents roughly 



BA 



one day, we conclude that for the earth is of the order of -^J-g-. 



-The true value of this quantity is .00328, the discrepancy resulting from 

 the imperfect rigidity of the earth. 



. MOTION OF A TOP 



254. As a second example of the methods of this chapter, let us 

 consider the motion of a spinning top. This we shall suppose to 

 be a solid of revolution spinning on a peg of which the end will be 



treated as a point, the contact between 

 the peg and the surface on which it 

 rests being assumed rough enough to 

 prevent slipping. The point of contact 

 is now a fixed point 0. Let us take 

 axes Ox, Oy, Oz fixed in space, the axis 

 of z being vertical, and also axes 1, 2, 

 fixed in the body, and coinciding witl 



the principal axes of inertia through 

 FIG. 150 



Let axis 1 be the axis of symmetry o 



the top, and let the moments of inertia about axes 1, 2, 3 be A, B, B 

 The first of Euler's equations becomes 



A d( l - 



JL - U, 



dt 

 since B = C and L = 0. Thus c^ is a constant, say H. 



Let the axis of the top cut a unit sphere about at a point whos( 

 polar coordinates are 1, 0, <, the axis of Oz being taken for pole, so 

 that is the angle between the vertical and the axis of the top. 



