Computes optimal semi-major axis and eccentricity control.

Four values of eccentricity are analyzed, [0 0.1 0.4 0.8]

Since version 7.
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Reference: Colin R. McInnes, "Solar Sailing: Technology, Dynamics and
     Mission Applications", Springer Praxis, London, 1999, pp. 136-148.
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See also Plot2D
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Contents

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%   Copyright (c) 2005 Princeton Satellite Systems, Inc.
%   All rights reserved.
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clear alphaStar; clear atan; clear labl;

True anomaly

%-------------
f = [0.01:0.05:2*pi];

Eccentricity

%-------------
e = [0.01 0.2 0.4 0.8];
for k = 1:length(e)
  labl{k} = ['e = ' num2str(e(k))];
end

for k = 1:length(e)
  alphaHat = atan2( (1+ e(k)*cos(f)) , (e(k)*sin(f)) );
  cA       = cos(alphaHat);
  sA       = sin(alphaHat);
  alphaStar(k,:) = atan( (-3*cA + sqrt(9*cA.^2+8*sA.^2))./(4*sA) );
end

r2d = 180/pi;
Plot2D( f*r2d, alphaStar*r2d, 'nu (deg)', 'Cone (deg)', 'Optimal Cone Angle for Changing SMA' );
legend(labl{:})

for k = 1:length(e)
  alphaHat = atan2( [(2 + e(k)*cos(f)).*cos(f) + e(k)./(1 + e(k)*cos(f))], sin(f) );
  cA       = cos(alphaHat);
  sA       = sin(alphaHat);
  alphaStar(k,:) = atan( (-3*cA + sqrt(9*cA.^2+8*sA.^2))./(4*sA) );
end

Plot2D( f*r2d, alphaStar*r2d, 'nu (deg)', 'Cone (deg)', 'Optimal Cone Angle for Changing Ecc' );
legend(labl{:})


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Published with MATLAB® R2020a