PROCEEDINGS 



THE ROYAL IRISH ACADEMY. 



PAPERS READ BEFORE THE ACADEMY. 



INITIAL MOTION. By JA.MES PATRICK JOHNSTON, M.A. 



[Read January 23, 1893.] 



Initiai Motion. 



The initial motion of a rigid body starting from rest under the action 

 of a system of finite forces ; and when the motion is constrained, the 

 initial values of the forces of reaction due to the constraints ; are 

 usuaUy deduced from the differential equations of motion of the second 

 order. In the case of constrained motion this method is tedious, for 

 it is necessary to differentiate the geometrical equations twice. The 

 initial motion and the initial reactions can, however, he obtained in 

 a comparatively simple manner by considering the momentum gene- 

 rated in a very small interval of time 8t. 



When we have proved in this manner any theorem concerning 

 initial motion, when the applied forces are finite, we are able at once 

 to write down the proof of the corresponding theorem for impulsive 

 forces. It is only necessary to change the notation. 



Fkee Motiox. 



"We will first investigate the initial motion of a rigid body starting 

 from rest under the action of any system of finite forces, when it is 

 not constrained in any way. 



E.I. A. PEOC, SEE, in., VOL. III. ^ 



