DYNAMICS OF A RIGID BODY. 155 



from Euler's theorem ( 64). If a body receive an im- 

 pulsive wrench on a screw r/ while the body is con- 

 strained to twist about a screw 0, then we have seen in 

 6 1 that the kinetic energy acquired is proportional to 



If 0i, 3 , 3 , 4 be the co-ordinates of referred to the 

 four principal screws of inertia belonging to the screw 

 complex of the fourth order, then ( 65, 67) 



Hence we have to determine the four independent varia- 

 bles 0j, 2 , 3 , 4 , so that 



shall be a maximum. This is easily seen to be the case 

 when 0!, 2 , 3 , 4 are respectively proportional to 



This method might be applied to any order of free- 

 dom, and of course gives the same result as 67. 



145. General Remarks. We shall here introduce 

 some general reflections upon the problem of the deter- 

 mination of the instantaneous screw corresponding to a 

 given impulsive screw. These reflections are called forth 

 by the circumstance that for the freedom of the fourth order 

 a different method of proceeding is required from that 

 which has been used for the second an third orders. 



It has been shown in 53 how the co-ordinates of 

 the instantaneous screw corres 



