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Moments of inertia about the center of mass of the system of six point masses

Find the moments of inertia about the center of mass of the system of six point masses.

clc;
clear all;
M = [10,10,8,8,12,12]; % [kg]
X = [1 -1 4 -2 3 -3];  % [m]
Y = [1 -1 -4 2 -3 3];  % [m]
Z = [1 -1 4 -2 -3 3];  % [m]
mt = sum(M);           % The total mass of this system

Three components of the position vector of the center of mass are

Xcg =(1/mt)*sum(M.*X);
Ycg =(1/mt)*sum(M.*Y);
Zcg =(1/mt)*sum(M.*Z);
V_cg = [Xcg,Ycg,Zcg]   % [m]
V_cg =

    0.2667   -0.2667    0.2667
Ig = [0.0,0.0,0.0;
      0.0,0.0,0.0;
      0.0,0.0,0.0];

The total moment of inertia is the sum of moments of inertia for all point masses in the system

for i =1:6
    x = (X(i) - Xcg);
    y = (Y(i) - Ycg);
    z = (Z(i) - Zcg);
    m = M(i);
 Ig = Ig + [  m*(y^2 + z^2),    -m*x*y,         -m*x*z;
             -m*y*x,             m*(x^2 + z^2), -m*y*z;
             -m*x*z,            -m*y*z,          m*(y^2 + x^2)]; % [kg*m^2]
end
Ig
Ig =

  783.4667  351.7333   40.2667
  351.7333  783.4667  -80.2667
   40.2667  -80.2667  783.4667

Published with MATLAB® 7.10

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