%%
% 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]
%%
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
%%
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