Path: Interplanetary/Insertion
% Simulate an optimal approach and orbit insertion at Mars (fmincon)
Treat the problem as planar. Models a fixed mass. fmincon is used to find the
optimal trajectory. This optimization is on the slow side and may take several
hundred iterations. If the thrust isn't high enough for the time given,
the acceleration will be maxed out - ones all the time - and there will
be a large error. When the thrust is more than enough, there will be a
coast period. The cost function will first increase until it plateaus and
then taper off to the final solution.
Parameter space:
0. Mass/thrust of the spacecraft
1. how long a time is allocated for the insertion burn (fTime)
2. the number of points along the trajectory
3. number of optimization iterations, or tolerances
Example solutions:
3500 kg / 40 or 20 N / fTime = 3 - coast time in trajectory
3000 kg / 15 N / 3
Note: lower thrust may require less mass, more points
The cost, f(x), is the total acceleration required for the maneuver. The
constraints, or Feasibility, are that the acceleration magnitude is less than
the maximum and that the final state is achieved at the endpoint.
Example output:
First-order Norm of
Iter F-count f(x) Feasibility optimality step
271 56026 8.140240e+01 5.301e-12 8.410e-01 3.252e-03
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See also ApproachCost2DMag, ApproachConst2DIneq, Simulate2DApproach
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Interplanetary: OrbitInsertion/ApproachConst2DIneq Interplanetary: OrbitInsertion/ApproachCost2DMag Interplanetary: OrbitInsertion/Simulate2DApproach Interplanetary: OrbitInsertion/TrueAnomalyStartHyperbola Orbit: OrbitCoord/RPRA2AE Orbit: OrbitCoord/RV2AE Orbit: OrbitMechanics/TimeOfFlightHyperbola Orbit: OrbitMechanics/VEscape SC: BasicOrbit/El2RV SC: BasicOrbit/Nu2M SC: BasicOrbit/VOrbit SC: Visualization/PlotPlanet Common: Database/Constant Common: General/DispWithTitle Common: General/HasOptimizationToolbox Common: General/Watermark Common: Graphics/Map Common: Graphics/NewFig Common: Graphics/Plot2D Common: Graphics/PlotDoubleYAxis Common: Graphics/TimeLabl Common: Graphics/XLabelS Common: Graphics/YLabelS Math: Linear/Cross Math: Linear/Dot Math: Linear/Mag Math: Linear/Unit
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