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Example 10.8, Orbital Mechanics for Engineering Students, 2nd Edition.

A satellite is to be completely despin using a two-mass yo-yo device with tangential release. Assume the spin axis of moment of inertia of the satellite is C = 200 kg · m^2 and the initial spin rate w0 = 5 [rad/s]. The total yo-yo mass is 4 kg, and the radius of the spacecraft is 1 meter.

clc;
C  = 200;       % [kg*m^2]
w0 = 5;         % [rad/s]
m  = 4;         % [kg]
R  = 1;         % [m]
K = 1 + C/(m*R^2); %     Nondimensional factor K

The required cord length l

l = R*(K)^0.5       %[m]
% Time t to despin
t = (K)^0.5/w0      %[s]
% Tension in the yo-yo cables
t = 0:0.001:5;
N = 2*K*C*w0^3*t./(R*(K + w0^2*t.^2).^2);
plot(t,N);
xlabel('time [s]');
ylabel('Tension N [N]');
grid on;
[maxN,i] = max(N);
l =

7.1414

t =

1.4283

The maximum tension in the yo-yo cables [N]; maxN
% which ocurs at
t = i*0.001  % [s]
maxN =

454.7542

t =

0.8260

The speed of the masses at release;

v = R*w0*(K)^0.5  % [m/s]
v =

35.7071

The angle rotated by the satellite during the despin;

theta = (pi/2 - 1)*(K)^0.5   % [rad]
theta =

4.0763

Cord length required for complete despin

l = R*(K^0.5 - 1)            % [m]
l =

6.1414

Published with MATLAB® 7.10