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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

 

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