Compute the torque due to the fusion engine magnetic dipole in Earth orbit

The engine is aligned with the velocity vector. The dipole is assumed to be along the X axis.

%--------------------------------------------------------------------------
% See also: BDipole, RVFromKepler, JD2000, U2Q, Plot2D, TimeLabl, Cross
%--------------------------------------------------------------------------

%--------------------------------------------------------------------------
%	 Copyright (c) 2016 Princeton Satellite Systems, Inc.
%  All rights reserved.
%--------------------------------------------------------------------------

% Define orbit
%-------------
rMag    = 6378.165 + 380; % Radius in km
p       = Period(rMag);
angle   = linspace(0,2*pi);
n       = length(angle);
dT      = p/n;
z       = zeros(1,n);
[r,v]   = RVFromKepler([rMag;0.5;0;0;0;0]);
uV      = Unit(v);
jD      = JD2000;


% Define array of magnets in fusion engine
%-----------------------------------------
uBody   = [1;0;0]; % Body vector of dipole
i       = 3.2e6;   % Current A
a       = 0.5;     % Radius (m)
nC      = 6;       % Number of coils
m       = pi*a^2*i*nC*uBody; % Dipole

% Compute over orbit using a loop
%--------------------------------
torque  = zeros(3,n);
for k = 1:n
  q           = U2Q(uBody,uV(:,k));
  b           = QTForm(q,BDipole( r(:,k), jD ));
  torque(:,k) = Cross(m,b);
end

[t,tL]  = TimeLabl((0:n-1)*dT);
yL      = {'T_x (Nm)' 'T_y (Nm)' 'T_z (Nm)', '|T|'};
s       = sprintf('Altitude %12.2f km',rMag - 6378.165);
Plot2D(t,[torque;Mag(torque)],tL,yL,s);

fprintf('DFD Dipole: %g\n',m(1));
fprintf('Max torque: %g Nm\n',max(Mag(torque)));


%--------------------------------------
% $Date$
% $Id: 7d40507ce324ee4fd5abeb53b37189151e69913d $

DFD Dipole: 1.50796e+07
Max torque: 472.198 Nm

Published with MATLAB® R2024a