## finding principal axis and moments of inertia tensor using eig function

on 27 Aug 2013

### Roger Stafford (view profile)

Good Morning,

I am trying to calculate the principal moment of inertia as well as the principal axis of inertia.

If I am given a tensor matrix of the rotational moment of inertia:

I=[Jx -Jxy -Jxz; -Jxy Jy -Jyz; -Jxz -Jyz Jz];

And wish to find the principal moments and principal axis of inertia then I would simply use matlab eig.

[Axes,Moments]=eig(I);

And then diagonal of the Moments matrix is the principal moments. Now say I want to find the cosine of the angle of the principal axis of inertia with the three axes X,Y,Z that are center at the CG...how would I go about this?

Is it cos(Axes(:,1)), cos(Axes(:,2)), cos(Axes(:,3)??

Thank you.

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### Roger Stafford (view profile)

on 27 Aug 2013

"Is it cos(Axes(:,1)), cos(Axes(:,2)), cos(Axes(:,3)??"

No, the components of the eigenvectors themselves, Axes(:,1)), Axes(:,2), Axes(:,3), are already the cosines of the angles between the three principal axes of inertia respectively and the x, y, and z axes, provided the eigenvectors are normalized.

Of course there is an ambiguity about the sense of each of these vectors depending on which of two opposite directions are to be considered as the positive directions of these axes of inertia.

Melissa

on 28 Aug 2013

Thank you!!!