I'm having an issue understanding how turtle geometry is supposed to work.
Let's say for the orientation vector O the Heading, Left, and Up unit vectors for the turtle are:
So the turtle is facing entirely in the x-direction.
If you wanted to rotate the turtle by some angle about the x-axis, such that the belly of the turtle would be rotating, you would take the RH matrix:
and multiply it by the orientation vector O like so:
So, clearly the turtle's orientation stays the same since it is facing directly on the x-axis. No rotation occurs. How is the "belly" of the turtle supposed to be rotated if you wanted to turn him upside down?