From (1.9) 
Hence 
_— = ' — 
J Sp + AX T+AT) J Gn> sl) p'(T) (Ax, f£AT) 
T 
lane 
; @, = pie) Sa ce <p mn 
where use has been made of (1.34). But by (1.27), FY pot = 0; so, 
JX + Axas T+AT) - J(x T) = p' Ax, ae (OB = jy (ie)ie) Aa 
T°? 
p'(T) AXn - HAT 
ad ite, b gin 
where the last equality results from (1.40). This gives 
J =p (1.43) 
and 
Jp 2-H (1.44) 
In the space of variables (Xp T), the vector p' is the gradient of 
the function J; it is normal to the surfaces of constant J; H is the 
Hamiltonian of the function J. This sheds new light on the maximal 
principle. Along an optimal trajectory, the change in cost J over a 
given time step AT is a minimum, that is, H is a maximum. 
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