Ellipsoid of inertia problem

K

Kremer

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Jun 5, 2008
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Hello, I'm solving a problem with the ellipsoid of inertia. The ellipsoid is described by radius of gyration tensor (RGT), which after diagonalization gives eigenvalues and within the diagonalization I'm obtaining also eigenvectors.

Now, I'm holding RGT, eigenvalues, eigenvectors. My question is, how it is possible to get orientation (or 3 angles of rotation respectively) of the ellipsoid, in the former reference system (before transformation to the principal axes), where are the coordinates of physical body related to.

I think the calculated matrices contain enough information, however I can't see the angles in it.

Thank you very much for helping in advance,
KK
 
Kremer said:
Hello, I'm solving a problem with the ellipsoid of inertia. The ellipsoid is described by radius of gyration tensor (RGT), which after diagonalization gives eigenvalues and within the diagonalization I'm obtaining also eigenvectors.

Now, I'm holding RGT, eigenvalues, eigenvectors. My question is, how it is possible to get orientation (or 3 angles of rotation respectively) of the ellipsoid, in the former reference system (before transformation to the principal axes), where are the coordinates of physical body related to.

I think the calculated matrices contain enough information, however I can't see the angles in it.

Thank you very much for helping in advance,
KK
Click to expand...

Suppose instead of ellipsoid - you had an elliptical plate (2-D problem).

How would you find it's moments of inertias? What would be the tensorial expression? What would the eigenvectors of the MI tensor mean?

How can you extend that method to 3D?
 
..well, i have found a solution for 2D problem and it's rather easy. i think the 3D is the issue, synce there is some axis reference system. additionaly, i am not sure about the geometrical meaning of the 'products of inertia' (xy,xz,yz,yx,zx,zy) in the tensor.

thanks in advance,
KK
 
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