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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