From the differential equation (1.1) 
Hence 
0=min {F+J£+ I} &t 
t iS ic 
Since dt > 0, 
On= mae {F + Jf + Jt CES) 
In order to find the minimum of the term in brackets, it is differ- 
entiated with respect to u and the result is set equal to zero. This is 
a necessary, but not sufficient condition; however, if one assumes a 
minimum, it serves the purpose. 
oe alamo) 0) (2.5) 
u x— 
Biya (Zi) 
we wy iad, = © @G)) 
x t 
Hence 
H =0 
u 
(1.43) 
JF ao BS = (i a Jf) 
From: (1.25) 
AL 
J, =p (1.42) 
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