Abstract
For any pair of three-dimensional real unit vectors
m
^
and
n
^
with
|
m
^
T
n
^
|
<
1
and any rotation
U
, let
N
m
^
,
n
^
(
U
)
denote the least value of a positive integer
k
such that
U
can be decomposed into a product of
k
rotations about either
m
^
or
n
^
. This work gives the number
N
m
^
,
n
^
(
U
)
as a function of
U
. Here, a rotation means an element
D
of the special orthogonal group
SO
(3) or an element of the special unitary group
SU
(2) that corresponds to
D
. Decompositions of
U
attaining the minimum number
N
m
^
,
n
^
(
U
)
are also given explicitly.
Cited by
13 articles.
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