182 



Summary of the Equations of Motion 



For convenience, the relevant defining relations are collected here: 



^ h dt^\|nr/ 



tan o^ = J \ = ^r * ^ 



(A) 



RH 



- ^ ^ - .. - ^f 



RR R r ^Q 



Srr = s, c; = cr^ = o-dog |) 



(B) 



V 



s;^ = z = V t 



U^ - 2Uft - v^ = 



H_ ♦ 2 U =0 



H R 



R(0) = a 

 (C) < H(0) = h 



In (a) the quantities on the left of the equations are defined in terms of 

 P> '^i V, (XClog jj), t, R, and H. The relations (B) constitute a differential 

 systera of third order in H, U, and R, so that (C) furnishes the necessary- 

 three initial conditions. In order to solve (B) it is necessary, in addition, 



to have an explicit functional fora for Cr(log rr) . For example, if the ideal 



n 



material is one which, does not work harden, then we have simply 



crciog |) = cr (28) 



where O is a constant, 



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