138 DYNAMICS OF A RIGID BODY. 



set in motion by the action of an impulsive wrench, the 

 kinetic energy which the body acquires is greater than 

 it would have been had the body been restricted to any 

 other screw of the complex than that one which it natu- 

 rally chooses. 



124. Reaction of the Constraints. An impulsive 

 wrench on a screw r; acts upon a body with freedom 

 of the third order, and the body commences to move by 

 twisting upon a screw 0. It is required to find the screw 

 A, a wrench on which constitutes the initial reaction of 

 the constraints. Let ^ denote the impulsive screw which, 

 if the body were free, would correspond to 9 as the in- 

 stantaneous screw. Then A. must lie upon the cylin- 

 droid (0, ij), and may be determined by choosing on 

 (0, r?) a screw reciprocal to any screw of the given screw 

 complex. 



125. Impulsive Screw is Indeterminate. Being given 

 the instantaneous screw 6 in a complex of the third 

 order, the corresponding impulsive screw rj is indeter- 

 minate, because the impulsive wrench may be com- 

 pounded with any reactions of the constraints. In fact 

 TJ may be any screw selected from a screw complex of 

 the fourth order, which is thus found. Draw the diame- 

 tral plane conjugate to a line parallel to 9 in the ellipsoid 

 of inertia, and construct the cylindroid which consists 

 of screws belonging to the screw complex parallel to 

 this diametral plane. Then any screw which is reci- 

 procal to this cylindroid will be an impulsive screw cor- 

 responding to 9 as an instantaneous screw. 



Thus we see that through any point in space a whole 

 cone of screws can be drawn, an impulsive wrench on 

 any one of which would make the body commence to 

 twist about the same screw. 



One impulsive couple can always be found which 

 would make the body commence to twist about any 



