Transcript DIRECTION COSINE MATRIX (DCM)

DIRECTION COSINE MATRIX (DCM)
b3
a3
b2
a2
a1
b1
ELEMENTARY ROTATIONS
ROTATION ORDER
TRANSPORT THEOREM
P
r
û3
û2
U
â3
wUA
û1
A
â1
â2
EULER ANGLES (BODY FIXED 3-2-1)
3
2
1
EULER ANGLE
REPRESENTATIONS
Euler Eigen Axis
Rotation Representations
Representation
Par.
Direction Cosine 9
matrix
Characteristics
•
•
•
Euler Angles
3
•
•
•
•
Applications
Nonsingular
Intuitive
Six redundant parameters
•
Analytical
studies
Minimal set
Clear physical representation
Trigonometric functions in
rotation matrix
Singular
•
Analytical
studies
Euler Angle Kinematics (3-2-1)
c3
DC
d3
b3
c3
a3
CB
3
.
d2
3
c2
.
b2
.
1
b2
2
2
1
c1
BA
a2
a1
b1
c1
b1