Analysis Used in Submerged Body Research 443 
Equations (C10) and (C11) reduce to 
Z = Er cos (C12) 
and 
Be i Ze arg. (C13) 
out 
Thus, the operation performed by the electronic system is equivalent to determining the 
Fourier coefficients of the fundamental of the gage signal. 
APPENDIX D 
Equations of Motion for Submarines 
The differential equations of motion in dimensional form, referred to a moving body axes 
system which is coincident with the principal axes of inertia and having the origin at the 
center of mass, can be written for the case when the submarine is initially in level flight and 
at a steady forward speed as: 
Axial Force 
° 3 0) = ' 1. 
m(u-vr+wq) = oat [xia =) evr it Ziwq] 
(uu) 
Lao 22 ' 2 ‘ 2 / ae 
+ 5¢u Xeses2)3s thee eeye et A seseyee | 
ae 
Lateral Force 
m(v-wp+ur) = 5 
Pp 2 rue ' : 
+t [¥.'u2 + Y'uv + ¥’.yvivl| 
‘ 
Clrlér) 
xe) 
U 
3 ‘ ' 
+—4 [viur+¥ ulr|8e+¥0\,,,)lvle+¥eup| 
i) 
a ae ue Le ah 
+ Se [¥:# + Y;p| +e - Y, 5, - (Fy): 
