Biology Reference
In-Depth Information
227
In three dimensions, translation is similar, i.e.:
x' = x
-
a,
y' = y - b,
and
z' = z
-
c.
Rotation is a combination of three two-dimensional rotations, i.e. obtaining
the coordinates by rotating around three axes separately. These angles of
rotation are referred to as Eulerian angles. Unfortunately, there is no
universally agreed convention of the sequence and direction of rotations.
One possible set of Eulerian angles,
and
gives the following rotation
matrix in three-dimension (Goldstein, 1950):
However, for the discussion of rotations for single bonds in polypeptides
and polynucleotides (Chapters 5 to 7), successive two-dimensional rotations
can be chosen to simplify calculations of atomic coordinates.
