286 



M. Poinsot on the Percussion of Bodies. 



Many other questions of the same kind might be proposed ; 

 these examples, however, will suffice, and we will proceed to a 

 more important problem from which numerous consequences 

 may be deduced. 



§11. 



Problem II. 



18. Let P, as before, be the force of impulsion given to the 

 body in a direction perpendicular to the plane of two of its prin- 

 cipal axes G X and G Y ; required the magnitude Q of the percus- 

 sion which the body would produce against an obstacle or fixed 

 point suddenly presented at any point D in the plane of these same 

 axes. 



Solution. — Let C be the point 

 in this plane where the impul- 

 sion P is applied : join C T), and 

 upon the production of this line 

 suppose a point to be so chosen 

 that, by striking at 0, no per- 

 cussion would be caused at the 

 point D. It is evident that if wi 

 the force P be resolved into two 



other parallel forces, one Q applied at D, and the other p applied 

 at 0, the required percussion at the point D will be exactly repre- 

 sented by the component Q immediately applied thereto ; for, by 

 hypothesis, the other component jo which strikes at O causes no 

 percussion upon the point D. Hence, in virtue solely of the 

 principle of the composition of parallel forces, the required per- 

 cussion Q at the point D in question will be expressed by 



Q=P 



CO 

 DO" 



To solve the problem, therefore, we have merely to determine 

 the position of the point O by means of the two points C and D. 



Now, in the first place, if a and b be the coordinates of the 

 point C, X and y those of the point D, and t and u those of the 

 point O, then, since is on the line which passes through C 

 and D, we have the equation 



._b-y 



■y= 



Xt-x) 



In the second place, in order that D may suffer no percussion 

 when the body is struck at 0, the spontaneous axis correspond- 

 ing to the latter point must pass through the former : hence this 

 second equation. 



