# Principal axis of inertia

In some slides of a robotics course I found the following text:

Principal axis of inertia u is a unit vector along a principal axis if I . u is parallel to u There are 3 independent principal axes!

I have these questions about it:

1. What is an axis of inertia?

2. What in this context is I?

• Moment of inertia Apr 3, 2017 at 20:29
• $I$ is the moment of inertia and the "principal axis of inertia" is often also referred to by "principal axis of rotation", which should clarify your first question Apr 3, 2017 at 20:41
• -1. No research effort. Apr 4, 2017 at 1:16
• While I could believe slide notes could omit it, I cannot believe a textbook would not introduce such an important variable.... Apr 4, 2017 at 10:15
• +1 and VtL for the brave try to clear an unclear textbook. Apr 5, 2017 at 19:45

In the context of your question, $I$ is once again the inertia tensor: that is, a tensor that allows you to compute, in general terms, the angular momentum of an object given the angular velocity. An inertia tensor can be decomposed into a rotation matrix and a diagonal matrix, the elements of which correspond to the principal moments of inertia. This is explained in the subtopic principal axes on the Wiki page for "moment of inertia".