148] PLANE REPRESENTATION OF DYNAMICAL PROBLEMS. 137 



but, by geometry, 



whence, 63, 



ft) GC 



x 



OA 



KI.HO .OA 

 HO.HA .OA 



A .HA 



3C ~i&amp;gt; j 



which is the required result. 



148. Energy acquired by an Impulse. 



The kinetic energy acquired by a given impulse, using the same notation 

 as before, is ( 91) proportional to 



Let A be the impulsive screw, and A the screw about which the body 

 is constrained to twist. Draw the chord AOH (Fig. 30), then, as A varies, 



Fig. 30. 



while A is fixed, the virtual coefficient of A and A varies as A H (63). 

 The square of this is proportional to AT, the length of the perpendicular 

 from A on the tangent at H. If PQ be the axis of inertia, the value of u* 

 is proportional to the perpendicular A Q, and, accordingly, the kinetic energy 

 acquired is proportional to 



AT 



