170 



CHAPTER XIV. 



THE DYNAMICS OF A RIGID BODY WHICH HAS FREEDOM 

 OF THE SIXTH ORDER. 



157. Introduction. When a rigid body has freedom 

 of the sixth order, it is perfectly free. The screw com- 

 plex of the sixth order includes every screw in space. 

 That there is no reciprocal screw to such a complex 

 is merely a different way of asserting the obvious pro- 

 position that when a body is perfectly free it cannot 

 remain in equilibrium, if the forces which act upon it 

 have a resultant. 



158. Impulsive Screws. Let A l9 A 2 , &c., denote a 

 series of instantaneous screws which correspond re- 

 spectively to the impulsive screws R l9 R 2 , &c., the body 

 being perfectly free. Corresponding to each pair Ai 9 RI 

 is a certain specific parameter. This parameter may be 

 conveniently defined to be the twist velocity produced 

 about At by an impulsive wrench on R i9 of which 

 the intensity is one unit. If six pairs, AiRi, A Z R Z , 

 &c., be known, and also the corresponding speci- 

 fic parameters, then the impulsive wrench on any 

 other screw R can be resolved into six impulsive 

 wrenches on R 19 &c., R 6 , these will produce six known 

 twist velocities on Ai 9 &c., A 6 , which being compounded 

 together determine A, the twist velocity about A, and 

 therefore the specific parameter of R and A. We thus see 

 that it is only necessary to be given six corresponding 

 pairs, and their specific parameters, in order to de- 

 termine completely the effect of any other impulsive 

 wrench. 



We are now going to show that z/ seven pairs a 



