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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