582 
ROTATION ROE STABILITY OR 
To determine 6, <p, if/ as functions of t } we have by equations (4), (5' 
and ( 6 ), and first from equation (5), 
d_/ST 
dt \8(p 
o 
0 , 
and therefore 
or 
ST _ 
— constant, 
00 
<p + cos Oij/ == r , 
a constant—the angular velocity of the body about the axis OC, which 
therefore remains constant during' the motion. 
Also from ( 6 ), 
l(M) = 0 ; 
therefore 
8T 
Sj, 
r = C u sill 2 0 0 + C 66 (0 + COS 6\j/) cos 0 
= c 44 sin 2 0\j/ + c 66 r cos 6 = G, . .(14) 
a constant—the angular momentum of the system about the axis of z. 
ST . . 
To obtain ^ we must differentiate the expression for T in terms of 
u } v, w y p, q, r; and therefore 
ST_STSu 8T8v STSr 
86 ~ 8u 86 + Sw S6> + + 8p 80 + Tq TO + ¥ 86 ' 
But 
and therefore 
Su 
8v 
^6 = — v> cos 0 , = w sin 0 j 
8w 
86 
ST 
86 
and 
ST 
S§ 
= u cos 0 — c sin 0 ; 
= (c 33 — c n ) (u cos 0 — v sin 0 ) w 
+ c 44 sin 6 cos 6 0 2 — c 66 r sin 6 0 
= sin 6 cos6(— - A') 
' c 33 c ll/ 
+ c 44 sin 6 cos 6y > 2 — c 66 r sin 00 , 
— c u61 
therefore equation (4) becomes 
c 44 0 — c 44 sin 6 cos 6 $> 2 + c 66 r sin 00 — .F 2 sin 0 cos 0 -— j — 0; ..,.(15) 
\ c 33 c iv 
