clM 



^ ^ dt 



/here F is the net force acting on S and F^ ' is the net force acting on S'. Since 

 F^'= I pnda = ~\ \^p{q-q)-p — nda 



7?l = j pqdr 



Fs = f lp(q- q)nc?a - f pi^n^a+^f p^dr 

 Js'2 Js' ^< r^K 



and 



we have 



[10] 



which is precisely the force in which we are interested. 

 At a point fixed with respect to the body, 



rf$ 



5$ 



= V ^ • y + 



dt dt 



[11] 



where v is the velocity of the point. As the origin is supposed stationary, and is also fixed 

 with respect to the body, the point being considered is in the most general case in rotation 

 about the origin, so 



[12] 



where u is the angular velocity of the body. We have 



r p^nrfa= [ p^nrfa+ f p (q 



J^, dt L' dt Jo' 



ca X r) n da 



We can write 



]^, dt dtJ^,"^ }^' dt dt ]^, J.. 



