3 
v denotes the linear angle formed by the plane, passing through Ox 
and Ox i, and the vertical plane, 8 the angle between Ox and Ox 
Let the projectile turning round the fixed point 0 be transposed so 
that S remains constant,* a> being the angular velocity round instantaneous 
axis OJ, and p, q, r , its projections on Ox, Oy, Oz. From the conditions 
regarding S, we get q = 0, i.e., OJ lies in plane xOx x . Therefore 
p = (o cos e, and r= — w sin e, where e is angle between OJ and Ox. 
Fig. 1. 
Let Gr denote the principal linear moment of all the quantities of 
motion ; its projections on Ox, Oy, Oz are Ap, 0, Br respectively, A 
being the moment of inertia of projectile relative to Ox, and B relative 
to equatorial axis passing through C. of Gr., hence Gr lies in plane zOx or 
xOx-l and 
Gr cos y = Ao) cos c = Ap ) ( 3 ^ 
Gr sin y= Boi sin On ) . ^ J 
where y is the angle between Gr and Ox. 
The angular velocity round Ox i will be 
dv 
dt' 
We will notice that 5 varies as the tangent passes from one position to the other. 
