Fees - [re nece =i cos 6 &dé 
Q Q 
=f {me001E0 + ieOVED 
— ULE 3 (mE OVE) + Gy EDP bE DVED 
+apgA cos 6} Edé (13) 
EQUATIONS OF MOTION, GENERAL 
Integrating the first term in Equations (7), (8), and (13) provides hydrodynamic forces 
and moments proportional to acceleration of the motion. These can be combined with the 
inertial terms of the rigid body to give the following equation of motion 
(M+M, sin? 9) Xa +(M, sin @ cos Nae =(QFysin 0)0 
= 1, +F, -Dcosd (14) 
(M, sin 6 cos 9) Xa +(M+M, cos” Ware -(Q, cos 0)0 
=17,+F,+Dsin@+W 
-(Q, sin 0)X og -(Q, C08 M%og + (1+1,)4 
= Fg -Dxg + Tx, 
where M,(t) = [ me.nay 
Q 
Q,(t) = of m,(£,t)Edé 
Q 
L(t) = We m, (£,t) £7 dé 
Q 
F, = F, -{-(M, sin? )%¢q -(M, sin @ cos 0)%og + (Q, sin 0)6} 
Ee alse {appropriate acceleration terms} 
Fg = Fo - {appropriate acceleration terms}. 
A detailed evaluation of the integral expressions for the hydrodynamic forces and 
moments is provided in Appendix A. 
