Path: StraightLine/SLPowerLimited
% Compute 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
the SLPLSolver function.
tau (1,1) Time between turnaround and tF (s).
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: Graphics/DistanceLabel Common: Graphics/Plot2D Common: Graphics/TimeLabl
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