Murthy 



i f ( + 3h i dl S 



M | V 001 00l' V *0100 , dz' 0100 , ^z ,y 



-8( ; oil- X '%ll )h(x '' 0) } x ' 



+ 2i 2 .. i '*,{,r 100 f 001 H-^oo-^oo' 

 ^'♦oooi - v *oooi ,» -ft] x ' 



x' / 



+ 2l*-. Ut pjg f()l0 r()oi -|5l-(i 010 -«'# 010 ) 



(ier* - V4» ) — — > x f 



v *0001 *0001 / d z' I 



-25aee 2lat * p (z -x'0 ) (iff* -V* )-^- x'ld 



V 001 00l' V 0001 *0001 / ^z' 



■v ' -J 



(III. 8) 



APPENDIX IV 

 RIGID BODY FORCES AND MOMENTS 



The rigid body force due to the weight and inertia of the ACV 

 is from (5. 3) 



f.« 



F R g ^ ) 



where U is the absolute velocity of an element of mass dm contain- 

 ed within the body V of the ACV. 



It is easy to show that 



f 



( U - gk ) dm = m ( U G - gk ) 



where m is the total mass of the ACV and U the absolute velocity 

 of its C. G. G 



lL = ( V + x ) A i + y j + zk 



206 



