guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
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2.4.2 Optimum Power Limited Rendezvous<br />
This analysis is concerned with a class of'vehicles which contain a<br />
rocket engine which is power limited <strong>and</strong> which has variable thrust by its<br />
ability to vary the exhaust velocity of the fuel. When operated at full<br />
(constant) power, the engine pay-off function for fuel consumption of such<br />
an engine is<br />
This pay-off function <strong>and</strong> the linearized equations of motion have been used<br />
to study low thrust <strong>flight</strong>s to Kars <strong>and</strong> Venus by Melbourne <strong>and</strong> Sauer (4-15)<br />
<strong>and</strong> by Gobetz (4-16). However, the analysis presented is due to Bryson (4-10).<br />
As is indicated from the title of Bryson's paper, (Reference 4-10)<br />
includes interception <strong>and</strong> soft l<strong>and</strong>ing. This capability is occasioned by his<br />
use of the cost function<br />
l/here<br />
p= relative separation<br />
_U= relative velocity<br />
L4= acceleration due to power limited engine<br />
to ,7-Z initial termina.1 time<br />
C n, C,are scalar weighting factors<br />
The linear differential equations for this problem are<br />
p' 3<br />
&=d_Btg<br />
where d = difference in acceleration due to gravity between vehicle <strong>and</strong><br />
target -f 4-a = 0 for rendezvous)<br />
Thus, the Hamiltonian of the problem is<br />
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