Why is there a difference in rotation coordinates?

Hallo, using Blender 2.72 I realize that standard meshes (shift A) … and then setting the rotation
to “Axis Angle” has values (0,0,1,0) ???
The 1 is rather disturbing in rotations around an axis (x,y,z) (all three values some float) … using Quaternions …

Does someone know the reason for this???

There are four components, WXYZ. It isn’t as simple as with XYZ eulers, in which each in X, Y and Z maps to an axis. You can actually change the Y = 1.0 to e.g. Y = 20 and nothing will change.

I would like to hear a human-understandable explanation by a math pro how it works!

When you are doing Euler rotations you typically have XYZ values. That means rotate X degrees around the X-axis (1, 0, 0), then rotate Y degrees around the Y-axis (0,1,0), then rotate Z degrees around the Z-axis (0,0,1).

The Euler rotations inherently have the axis vectors built into the equations. In ‘axis angle’ you supply a single vector and a rotation amount. At least one of the XZY coordinates has to be non-zero in ‘axis angle’ mode because a vector of length 0 does not point anywhere.

What a superb serie of all one could/should know about rotation and rigging ! Super. Thanks!