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Spin axis, precession
Example 10.2, Orbital Mechanics for Engineering Students, 2nd Edition.
A cylindrical shell is rotating in torque-free motion about its longitudinal axis.
r = 1; % [m] l = 3; % [m] m = 100; % [kg] theta = 20; % [deg ]nutation angle % How long does it take the cylinder to precess through 180 ° if the % spin rate is 2*pi/radians per minute ws = 2*pi; % [rad/min] C = m*r^2 % [kg*m^2] A = 1/2*m*r^2 + 1/12*m*l^2
C = 100 A = 125.0000
A > C, Direct (prograde) precession
wp = C/(A - C)*ws/cosd(theta) % [rad/min]
wp = 26.7457
The time for the spin axis to precess through an angle of 180 ° is
t = pi/wp*60 % [sec]
t = 7.0477
Published with MATLAB® 7.10