Home » Space Flight/Orbital Mechanics Excercise » Moments of inertia about the center of mass of the system of six point masses

# 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