Thanks for advices.
I must honestly say that I am a little bit drunk while writing this post, so please forgive me errors and everything.
Madhogo! He/You have touched very interesting topic (btw it is not me who downoveted post).
Determinant was put there deliberately and with full consciousness! Once I had to write a program that draws multidimensionl cubes (I have attached screenshot to give you better picture of what I am talking about). When I faced this problem I realize that rotation is actually performed on a plane, not around axis. Rotation around axis is an artificial being, which works only in 3 dimensions. Things are much more consistent and general if you use determinants. If you take a look at cross product you will find that out it consists of 3 determinants, one for each plane. You can describe rotations in 3 dimensions using determinants and this is IMO more natural, consistent and general than using cross product. In 2d you have one plane, in 3d you have 3 planes (although 2 are sufficient to rotate point to any position - I exploited this to limit number of sliders in my old Cube ?D program), in 4d you will have 6 planes (but again 3 are sufficent) and so on.
Moment of inertia on the other hand can be described by principal moments. So for 3 dimensional space it can be a 3-vector (x, y, z). If I will be able to expand my engine to 3d (or maybe even experiment with more dimensions...?) I will rather follow this path, because things seems to be much simplier. So this is why I am using determinant and real number, not because I limited myself to 2d, but paradoxically opposite, as from my earlier experiences it seems.
cube5d.png 20.51KB 13 downloads
PS. A and B are not limited to (r, n), (r, n, p) nor (r, n, p, L). They are ultimately numbers. In fact I was already exprimenting with soft bodies, but this is another chapter (leads to cool reminiscence of Mach's principle).