Path: FormationFlying/EccDynamics
% Compute velocities for periodic motion in an eccentric orbit
Given an initial Hills state (xH0) at a particular true anomaly (nu0) of an
eccentric orbit (e), compute the in-plane velocities (dx and dy) required for
periodic motion.
Use any of the following methods:
1) symmetric - Motion is symmetric in-track about the origin
2) fuel optimized - Use LP to find minimum of abs(dx) + abs(dy)
3) velocity constraint - Leave dx = dx0, solve for new dy
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Form:
[D, dx, dy] = FFEccDMatPeriodic( xH0, nu0, e, method );
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Inputs
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xH0 (6,1) Initial state in Hills frame
nu0 (1,1) True anomaly (at initial state) [rad]
e (1,1) Eccentricity
method (1,1) Indicate which method to use
1 - symmetric
2 - fuel optimization
3 - velocity constraint
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Outputs
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D (6,1) Vector of integration constants
dx (1,1) Scaled radial velocity required for periodic motion
dy (1, ) Scaled along-track velocity required for periodic motion
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References: Inalhan, Tillerson, How, "Relative Dynamics and Control of
Spacecraft Formations in Eccentric Orbits", Journal of Guidance,
Control & Dynamics, Vol.25, No.1, Jan-Feb 2002.
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FormationFlying: EccDynamics/FFEccDH FormationFlying: EccDynamics/FFEccRMat Common: CommonData/SwooshWatermark Common: General/CellToMat Common: General/MatToCell Common: General/Watermark Common: Graphics/NewFig Common: Graphics/Plot2D Common: Graphics/PltStyle
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