RELAY ARMATURE REBOUND ANALYSIS 



193 



where 



Cn = (fi + 1) Cu = C31 = fif3 



C22 = (^2 + 1) Cn = C21 = (1 - (iQ 



C33 = (d + 1) C23 = C32 = -(ojz 



(3) 



Xw , i;2o , 2:30 are the initial velocities, .Xio , X20 , 2:30 the initial displace- 

 ments for the free interval in question. Interpretation of the analytic 

 results is simplified by the introduction of normalization. Let Xa be Xi 

 just before the "zero" impact and define 



Vi 



— . ■> Xx 

 XaT XaVl 



Xain 



Vi = 



d ^ Xi 



Xa 



(9 



Fi 



(2) 



Dividing Equations (d) by XaT yields the normalized equations of 

 motion: 



621 + 622-^ +623^ J 



C31 + C32^+C33^j 



+ 2/10 ( - ) + 2/10 



+ 2/20 ( - ) + 2/20 



-) + 2/30 ( - ) + 2/30 



(1) 



(2) Impact Interval 



The change of velocity at point "i" due to an impact at "f" is, by 

 definition of the coefficient of restitution " fc" : 



Axi = — (1 + ki)xi (e) 



Since this velocity change occurs as rotation about the conjugate 

 point as an instant center of rotation, the impact relationships may 

 be written, for an impact at point "1", 



Ail = — (1 + ki)xi 



AX2 = — (1 + ki)xi 



(f - ••') 



