Eigenvectors of a moment of inertia tensor

Neil3030

What exactly does the eig(X) function in MATLAB output, when X is a moment of inertia tensor? As in, what would these figures actually represent (in language appreciable to the non physicist!)

So, for example I created a triangle with coordinates (0,0),(1,2) and (5,0). And plot it as so:

clear all;close all
x1=0;
y1=0;
x2=1;
y2=2;
x3=5;
y3=0;

h=plot(x1,y1,'ro','markersize',2,'MarkerFaceColor','r');hold on;
h=plot(x2,y2,'ro','markersize',2,'MarkerFaceColor','r');
h=plot(x3,y3,'ro','markersize',2,'MarkerFaceColor','r');

axis([-(max([abs(x1),abs(x2),abs(x3)])+.5) max([abs(x1),abs(x2),abs(x3)])+.5...
    -(max([abs(y1),abs(y2),abs(y3)])+.5) max([abs(y1),abs(y2),abs(y3)])+.5]);

axis('square');

line([x1,x2],[y1,y2],'color','k');
line([x1,x3],[y1,y3],'color','k');
line([x2,x3],[y2,y3],'color','k');

I next compute the inertia tensor as follows, assuming Ixz and Iyz to be 0 (is it ok to do this actually?):

Ixx=((y1^2)+(y2^2)+(y3^2));
Iyy=(x1^2+x2^2+x3^2);
Izz=((x1^2+y1^2)+(x2^2+y2^2)+(x3^2+y3^2));
Ixy=((x1*y1)+(x2*y2)+(x3*y3));
Ixz=0;
Iyz=0;


I=[Ixx Ixy Ixz; Ixy Iyy  Iyz; Ixz Iyz Izz];

and finally run the function to extract the eigenvectors

[d,v]=eig(I)

This returns d as:

-0.9960    0.0898         0
    0.0898    0.9960         0
         0         0    1.0000

what do these values actually mean, to the layman? and is what I've done acceptable?

Thanks!

Morbert

They are the principle axes of your rotating system.

Physically speaking, they are axes in which the mass of the system is evenly distributed around.