142] PLANE REPRESENTATION OF DYNAMICAL PROBLEMS. 129 



of inertia to H. But, as A is the only screw reciprocal to H, it is necessary, 

 by the theorem just given, that an impulsive wrench on A must make the 

 body commence to move by twisting about A . 



Fig. 22. 



As and are fixed, it follows from a well-known theorem, that as 

 otherwise proved in 137, A and A form two homographic systems. 



141. Twist Velocity acquired by an Impulse. 



We can obtain a geometrical expression for the twist velocity acquired 

 about A by a unit impulsive wrench on A (Fig. 22). 



It appears, from 90 (see also 147), that the twist velocity acquired 

 on cc by an impulsive wrench on 77, is proportional to 



2 



The numerator being the virtual coefficient is proportional to AO.A H 

 ( 68), and as u^ is proportional to A O .A H ( 134), we see that the 

 required ratio varies as AO -f- A O which itself varies as 



HO 

 HO 



hence we obtain the following theorem : 



The impulsive wrench on A, of intensity proportional to HO, generates a 

 twist motion about A , with velocity proportional to HO . 



The geometrical representation of the effect of impulsive forces is thus 

 completely determined both as regards the instantaneous screw, and the 

 instantaneous twist velocity acquired. 



142. Another Construction for the Twist Velocity. 



A still more concise method of determining the instantaneous screw can 

 be obtained if we discard the points and , and introduce a new fixed 

 point, ft, also on the homographic axis. 



B. 9 



