KINETICS OF A RIGID BODY. [298. 



-where x,y are the co-ordinates of the centroid ; and 



z = Ew + Deo 2 , 



x = a&myz aPSmzx = Diet Ea> 2 , 

 y yx) = a&mx 2 aP^mxy + a&my* + w^mxy = Ceo, 



where C=2m(x 2 +y 2 ), D = *Zmyz, E=^mzx are the notations 

 introduced in Art. 255. 



With these values the equations of motion assume the form : 



- Myu = ?.X+A X + B x , 



-zY)- aA y - 

 -xZ] + aA x 



298. The last equation is identical with equation (i). 



The components of the reactions along the axis of rotation 

 occur only in the third equation, and can therefore not be found 

 separately. The longitudinal pressure on the axis is 



= -A.-S.=*Z. 



The remaining four equations are sufficient to determine A t 

 A y , B x , B y . 



The total stress to which the axis is subject, instead ol: being 

 resolved into two forces, at A and B, can be reduced for the 

 origin O to a force and a couple (see Fig. 34). The equations 

 (4) give for the components of the force 



-A X -B X = 2X+ 



(5) 



This force consists of the resultant of the external forces, 

 R = 



and two forces in the ^/-plane which form the reversed effective 

 force of the centroid ; for Mxw 2 and MyuP give as resultant the 



