Path: Orbit/StraightLine
% Returns trajectory for an ideal power-limited rocket (straight-line)
If there are no outputs the function produces two plots.
Power limit is the only constraint; thrust and exhaust velocity can go to
zero or infinity. Uses Leitmann's 1961 result that the optimal
acceleration profile is linear in time. The optimal can be either:
* Constrained fuel and time, maximized distance OR
* Constrained distance and time, minimized fuel OR
* Constrained fuel and distance, minimized time.
The acceleration profile is:
a(t) = A*(tF-tau-t)
a is acceleration, A is a constant, tau is a constant, t is mission time,
tF is the final time.
Type SLPLTrajectory for a demo.
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Form:
SLPLTrajectory( d ); % create plots
[t,d,v,a,m,uE,T] = SLPLTrajectory( d );
[t,d,v,a,m,uE,T] = SLPLTrajectory( A, tau, Pj, m0, tF, t, doPlot )
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Inputs
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A (1,1) Acceleration scale parameter, (m/s^3). Find this using
another SLPLFind function, such as SLPLFindMass.
tau (1,1) Time between turnaround and tF (s). Find this using
another SLPLFind function, such as SLPLFindMass.
Pj (1,1) Jet power (eta*P, eta*sigma*mE) (W)
m0 (1,1) Initial (wet) mass (kg)
tF (1,1) Final time (s)
t (1,:) Time vector (optional) (s)
doPlot (1) Flag to create plots
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Outputs
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t (1,:) Time vector (same as argument, if given) (s)
d (1,:) Distance at t (km)
v (1,:) Velocity at t (km/s)
a (1,:) Acceleration at t (m/s^2)
m (1,:) Mass at t (kg)
uE (1,:) Exhaust velocity at t (km/s)
T (1,:) Thrust at t, (N)
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Reference: Leitmann, George. "Minimum Transfer Time for a Power-Limited
Rocket." Journal of Applied Mechanics 28, no. 2 (June 1,
1961): 171-78. https://doi.org/10.1115/1.3641648.
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Common: CommonData/SwooshWatermark Common: General/CellToMat Common: General/MatToCell Common: General/Watermark Common: Graphics/DistanceLabel Common: Graphics/NewFig Common: Graphics/Plot2D Common: Graphics/PltStyle Common: Graphics/TimeLabl
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