guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
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The Hsmiltonian for the problem is:<br />
H = P’i =/+Art&)<br />
But, the Pontryagin Msximum Principle states that the function e(t) which<br />
minimizes the coast, #(t> , is that function which causes the Hamiltonian<br />
be a maximum at each instant of time. Therefore, this value of 8 can be<br />
to<br />
found by setting the derivative<br />
d/4<br />
dH/dB equal to zero:<br />
or<br />
dB<br />
=-$aodjnB tGao cbo~ =o<br />
The Pi are the co-state variables <strong>and</strong> obey the differential equations:<br />
or<br />
q-0,<br />
Since, the boundary condition on Pl is:<br />
or<br />
And since P, =<br />
pczp=o<br />
0, the solution for Pl (t) is:<br />
/9 (t) = 0<br />
Solving the differential equations for P3 <strong>and</strong> P4 with P1 = 0 gives<br />
<strong>and</strong> the steering law becomes:<br />
or letting<br />
tLwe = c, f c- t<br />
77<br />
(4.38)