By way of contrast he notes that Felix Klein appears not to look beyond the theory of Quaternions and spatial rotation.
12.
In the case of spatial rotations, SO ( 3 ) is topologically equivalent to three-dimensional real projective space,.
13.
Note that the GEM equations are invariant under translations and spatial rotations, just not under boosts and more general curvilinear transformations.
14.
Hence a selective merge of say, just the definition, to Versor or Quaternions and spatial rotation is an obvious alternative to deletion.
15.
An example of the three parameters that specify a spatial rotation are the roll, pitch and yaw angles used to define the orientation of an aircraft.
16.
There's an article on quaternions and spatial rotation which may be helpful .-- talk ) 20 : 41, 6 March 2008 ( UTC)
17.
Very similar formulas can be found in the article on quaternions and spatial rotations, which covers this from a purely mathematical viewpoint but does not cover electromagnetism.
18.
There is a natural 2-to-1 homomorphism from the group of unit quaternions to the 3-dimensional rotation group described at quaternions and spatial rotations.
19.
In mathematical terms, a Lorentz transformation can be separated into the product of a spatial rotation and a " proper " Lorentz transformation which involves no spatial rotation.
20.
In mathematical terms, a Lorentz transformation can be separated into the product of a spatial rotation and a " proper " Lorentz transformation which involves no spatial rotation.
