/sci/ - Science & Math » Thread #14232251

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Anonymous Tue 15 Feb 17:48:53 2022 No.14232251 View Reply Original Report

Quoted By: >>14232453

What do the products of inertia in the inertia tensor mean and what happens when they're 0? Would a rotation around such axis not work?

Anonymous

Anonymous Tue 15 Feb 2022 18:36:27 No.14232400 Report

Quoted By:

Do you know what diagonalizing a matrix means? The three eigenvectors are known as principal axes and are the most natural axes for a body to rotate around in some sense. An element of the tensor vanishing might not matter, but if one of the eigenvalues vanishes then that usually means that sum of torques about that axis must always be zero, and the rotation of the body is not determined. A common example in physics problems is the idea of a "massless pulley" that rotates however it needs to for the problem to work out and the tension on both sides is exactly the same.

Anonymous

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Anonymous Tue 15 Feb 2022 18:50:41 No.14232453 Report

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>>14232251
The products of inertia are zero if and only of the axis chosen is a PRINCIPLE axis. That is, its an eigenvector of the inertia tensor. Motion about an acist that is NOT one of these, tends to be unstable.
>Would a rotation around such axis not work?
Yes, they work. Any arbitrary inertia tensor can be diagonalized, because they are real and symmetric.

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