DYNAMICS OF A RIGID BODY. 167 



impulsive wrench, and let be the screw about which the 

 body would commence to twist in consequence of this 

 impulse if it had been perfectly free. 



The body when limited to the screw complex of the 

 fifth order will commence to move as if it had been free, 

 but had been acted upon by a certain unknown wrench 

 on X, together with the given wrench on t|. The move- 

 ment which the body actually acquires is a twisting 

 motion about a screw which must lie on the cylindroid 

 (, p). We therefore determine to be that one screw on 

 the known cylindroid (, p) which is reciprocal to the 

 given screw X. The twist velocity of the initial twisting 

 motion about 9, as well as the intensity of the impulsive 

 wrench on the screw X produced by the reaction of the 

 constraints, are also determined by the same construc- 

 tion. For by 17 the relative twist velocities about 0, , 

 and p are known ; but since r/' is known, the twist velocity 

 about is known ( 60) ; and therefore, the twist velo- 

 city about is known ; finally, from the twist velocity 

 about p, the intensity X" is determined. 



155. Analytical Investigation. A quiescent rigid body 

 which has freedom of the fifth order receives an impul- 

 sive wrench on a screw r\ : it is required to determine the 

 instantaneous screw 0, about which the body will com- 

 mence to twist. 



Let X be the screw reciprocal to the freedom, and let 

 the co-ordinates be referred to the absolute principal 

 screws of inertia. The given wrench compounded with 

 a certain wrench on X must constitute the wrench which, 

 if the body were free, would make it twist about 0, whence 

 we deduce the six equations (h being an unknown 

 quantity). 



hpiQi = rf'tji -f X"Xi 



&c., &c., 

 h$s = /V, + X"X C . 



