I 



Ball — Dynamical Problems of the Theory of a Rigid Body. 37 



The result is, therefore, one of very great simplicity, and the 

 geometrical solution of the problem is now quite complete. Being- 

 given the impulsive screw corresponding to P, we find P' by draw- 

 ing PXL and L YP' : then to produce an unit twist velocity on P', 

 the intensity of the impulsive wrench must be proportional to LX 

 ■=7 LY. More simply still, by a proper choice of units, LX will be 

 the intensity of the impulsive wrench, and L Y the acquired twist 

 velocity. 



It can also be shown that the chord joining A and P' is divided by 

 the homographic axis at Z, so that the ratio of PZ to PX! varies pro- 

 portionally with the square of the twist velocity about P' produced by 

 the unit of impulse on P. 



The line PP' envelops a conic, and the point of contact divides 

 PP' into two segments, whose ratio is proportional to the square of 

 the twist velocity acquired by an impulsive wrench of unit intensity. 



