A Level Maths Notes: FP4 – Rotation Matrices in Three Dimensions
The matrix representing a general rotation in three dimensions is
This is a complicated matrix but for rotations about one of the coordinate axes it simplifies considerably.
A rotation about the
-
axis fixes
We need a 1 in the top left hand corner and zero's in the first row
and column. Take
to
give.
A rotation about the
-
axis fixes
We
need a 1 in the middle and zeros in the second column and row.
Take
to
give
A rotation about the
–
axis fixes
We
need a 1 in the bottom right hand corner and zeros in the third
column and row. Take
to
give
The angles
are
called Euler angles. The general rotation matrix can be obtained by
multiplying the three rotation matrices together.