178 M. Poinsot on the Percussion of Bodies. 



VI. On certain new and remarkable centres in moving 



BODIES. 



31. Let us suppose that the body really comes into collision 

 with an obstacle or fixed point C at the distance x from the 

 centre of gravity G ; the component Q will be destroyed, and 

 the body will remain under the sole influence of the component 

 p applied at 0'. This force ^j will act upon the body just as if 

 the latter were free ; for the point C, where the obstacle was 

 presented, being the spontaneous centre with respect to the point 

 0', considered as a centre of percussion, it is evident that the 

 obstacle cannot in any way alter the effect of the force p. 



Thus the body which, before collision, was animated by the 

 force P applied at the distance h from the centre of gravity G, 

 will, after the shock, move under the influence of a new force, 

 _P£-P^ 

 ^~ is^ + K^ 



applied at the distance from the same centre G. 



The original velocity of the centre of gravity, which was 

 P 



will therefore be changed to another u', where 



u' 

 or replacing PA by MK^^, 





, ux'^—'K?6x ,,. 



" = -^Mle^' ^^^ 



and the original rotation, which was 



will be changed to 



xMY^^~ ^2 + K2 ' ' ' \'^) 



82. This being established, several simple and easily answered 

 questions suggest themselves. 



In the first place we may inquire at what distance x, that is 

 to say, at what point C must the obstacle be presented in order 

 that, after impact, the centre of gravity of the body may move 

 in an opposite direction — in fact rebound — or may proceed on- 

 ward with the greatest possible velocity or, if we please, with 

 any given velocity whatever. 



In the second place we may ask at what point the obstacle 



