THE AERODYNAMICS OF A SPINNING SHELL. 
32 7 
instant is represented by the vector 0 , with components 0 1( 0 2 , 0 3 . The direction of 
the axis of the shell OA is represented by the unit vector* A, and the direction of 
motion of the centre of gravity by the unit* vector X. 
2 
With the notation already introduced in Part I., the total angular momentum of 
the shell can be expressed as the sum of two vectors :— 
(i.) The angular momentum about OA, ANA ; 
(ii.) The total angular momentum about a transverse axis. 
If the total angular velocity about a transverse axis is W, the angular momentum is 
BiU, and is equal to the moment of momentum of a particle whose mass is B and 
whose distance from 0 is represented by the vector A. Now the actual velocity of 
such a particle relative to O is A'—[A . 0], and therefore its moment of momentum 
about O is 
B {[A . A'] — [A . [A . 0]]}. 
The total angular momentum, H, of the shell about O is therefore given by the 
equation 
(3.101) H = ANA+B {[A . A']-[A .[A. 0]]} ; 
using (3.012) this becomes 
(3.102) H = ANA + B {[A . A 7 ] — (A . 0) A + 0}. 
VOL. CCXXI.-A. 
* I.e. (A) 2 = (X) 2 = 1. 
2 z 
