WOLFRAM|DEMONSTRATIONS PROJECT

Combining Two 3D Rotations

​
angles of rotation A & B
angles for axes of rotation
θ
A
ϕ
A
θ
B
ϕ
B
Set
:Lists {pts,poly} and {{8.,4.,2.,6.},{8.,6.,5.,7.},{8.,7.,3.,4.},{4.,3.,1.,2.},{1.,3.,7.,5.},{2.,1.,5.,6.}} are not the same shape.
The concentric rotations
A
and
B
can be combined either by doing
A
first and then
B
, written as
B∘A
, or
B
first and then
A
, written as
A∘B
. This right-to-left notation comes from the algebra of dot products,
M
B
·
M
A
·v
and
M
A
·
M
B
·v
, where
v
is a vector and
M
A
and
M
B
are the matrices representing the rotations
A
and
B
.
In general,
A∘B≠B∘A
.
You can vary the axes of rotation by changing the spherical coordinates of their corresponding vectors.