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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 = 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