i66 



KINETICS OF A RIGID BODY. 



[307. 



307. To determine the impulsive stress produced on the axis 

 by a single impulse F, let us write out the general equations 

 of the impulsive motion. 



Take the fixed axis as the axis of z and the ^jtr-plane through the 

 centroid G (Fig. 36), and let ^, o, o be the co-ordinates of G, and 



z 

 B* 



*B 





z \ tnose f tne point o; 



v 



1/7 



X 



Fig. 36. 



application P of the impulse 

 The components of F may be 

 denoted by X, Y, Z ; those o 

 the reactions of the axis by A x 

 A y , A z , B x , B y , B g , similarly as 

 in Art. 296. 



~ As the initial motion after 

 impact is a rotation about the 

 axis of z, we have x= c 

 y = <ax, 2=0, so that the mo 

 mentum of a particle of mass 

 m has the components may, max, o. Reducing these mo 

 menta to the origin (9, we find a resultant momentum whose 

 components are w^my=o, <&mx=Mwx, o; and a resulting 

 couple whose vector has the components co^mzx=L 

 (t)^myz=D(D, a)^m(x^-\-y 2 ') = C(i) ) where C, D, E have the 

 same meaning as in Art. 297. 



The six equations of motion just after the impulse are there 

 fore, if the body was originally at rest : 



(14) 



Ca=x 1 Y-y 1 X. 



308. The last of these equations is nothing but the equation 

 (i i). The components A,, B, along the axis cannot be deter- 



Y+A y +B yt 



z^ Y aA y bB y , 



