RELAY ARMATTHE REBOUND ANALYSIS 



195 



is a convergent series and approaches, for a complete series: 

 2 . . -7 



Lim-d + k + /v- + 



n— »M O 



k"] 



C(l - k) 



(10) 



The maximum rebound amplitude in any interval is — yio„/2C. 

 The maximum excursion occurs during the first bounce at t' = 1/C and 

 equals — k /2C. 



Appendix III 



ANALYSIS OF REBOUND PATTERNS^ — T\VO-DEGREE-OF-FREEDOM SYSTEM 



The equations of motion of this system are 



yi = ^At'^ + yiont' + yion 



y2 = ^Bt'^ + yiOnt' + 2/20n 



where A = Cn ^ Cuf 

 B = Cu + C722/ 



(g) 



, _ t measured from the start of the par- 

 7" ticular free interval in question. 



A. Complete Front Series 

 At the beginning of a front series 



1/1 = 



yi = 2/leO 

 y2 = 2/2eO 

 2/2 = heO 



(h) 



(i) 



In a manner analogous to that for the one-degree-of-freedom system 

 each front impact reduces 2/1 to —kiyi . Therefore, after the n*'' impact, 



in. 



yion — —i^iyieo 

 and the time elapsed in the n^^ interval is 



In = —r- yuo 



(J) 



