Post on 23-Jan-2022
Euler Angles
According to Euler's rotation theorem, any rotation may be described using three angles. If the rotations are written in terms of rotation matrices B, C, and D, then a general rotation can be written as A=DCB.
Rotations around the z�x�z axes.
cos sin 0
sin cos 0
0 0 1
B
φ φφ φ
− =
1 0 0
0 cos sin
0 sin cos
C θ θθ θ
= −
cos sin 0
sin cos 0
0 0 1
D
ψ ψψ ψ
− =
cos( ) sin( ) sin( ) cos( )
cos( )
cos( ) cos( ) sin( )
cos(
- - -
+ -
cos( ) sin( ) cos( ) sin( ) sin( )
sin( ) cos( ) sin( ) cos( )) cos( ) sin( )
sin( ) sin( ) cos
sin( ) sin( ) cos( )
sin( ) cos( )
o (- )+ c s
CBDA
θ θ θθ θ θ
θ
φ φ φ φφ φ φ φ
φ φ
ψ ψ
θ
ψ ψ ψψ ψ ψ ψ ψ
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅
=
=( )θ
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