2 4 8.] 



PLANE MOTION. 



135 



247. The instantaneous centre being the point whose velocity 

 is zero at the given instant, we find its co-ordinates X Q , y^ from 

 the equations 



o = v x , - ( j/ -/) o>, o = zv + (*b -*') co, 



whence 





(4) 



By eliminating t between these equations, the equation of the 

 space centrode can be found. 



The co-ordinates f , ?7 of the instantaneous centre referred to 

 the moving axes are found in a similar way from the equations (2) : 



cos 



cos e + v, sin 0), (5) 



from which the body centrode can be found by eliminating t. 



248. In Arts. 245 and 246 expressions were found for the 

 component velocities v x , v y parallel to the fixed axes Ox, Oy. 

 To find the component velocities 

 v& v^ parallel to the moving axes 

 <9f, Or], let x, y be the co-ordi- 

 nates of any point P with respect 

 to the fixed axes (Fig. 55), , rj 

 those with respect to the moving 

 axes, and let 6 be the angle xO%. 

 The velocity of P parallel to the 

 axes O%, Or) consists of two parts, 

 that arising from the motion of P relative to f Orj whose com- 

 ponents are of course d%/dt, dy/dt, and that due to the rotation 

 of the moving axes. The components of the latter velocity are, 

 by (i), Art. 245, cor), cog. Hence 



Fig. 55. 



dt 



dt 



(6) 



