Path: SCPro/Landers
% Bilinear tangent law for orbit insertion or landing.
Assumes constant acceleration of gravity and constant engine
acceleration. For applicable landing or takeoff problems the first
is true, the latter is usually not due to the decrease in mass of the
vehicle. The thrust angle is from the horizontal and g is along
the vertical. It uses fminsearch to find the optimal angles.
The launch or landing vector may not be vertical.
Type BilinearTangentLaw for a demo from the reference.
Units may be of any type as long as they are consistent.
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Form:
[beta, t] = BilinearTangentLaw( u, g, a, h, n, opt, dT )
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Inputs
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u (1,1) Final or initial velocity
g (1,1) Acceleration of gravity
a (1,1) Engine acceleration
h (1,1) Final or initial altitude
n (1,1) Number of steps
opt (1,:) fminsearch options
dT (1,1) Time step in place of n
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Outputs
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beta (1,n) Thrust angle from horizontal
t (1,n) Corresponding time vector
tMin (1,1) Minimum time
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Reference: Arthur E. Bryson, Jr., Y. C. Ho, "Applied Optimal Control:
Optimization, Estimation, and Control," Orbit, pp. 83-86.
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Common: Graphics/Plot2D
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