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Euler Angles
Input values
Euler rotation sequence | yaw-pitch-roll (3-2-1) first rotation | 30° (degrees) second rotation | 15° (degrees) third rotation | 20° (degrees)
Direction cosine matrix
C=(0.837 | 0.483 | -0.259 -0.393 | 0.858 | 0.330 0.382 | -0.175 | 0.908)
Principal rotation parameters
Φ | 36.8° (degrees) e^^ | (0.422 0.535 0.732)
Euler parameters (quaternions)
β_0 | 0.949 β_1 | 0.133 β_2 | 0.169 β_3 | 0.231
Cayley-Klein parameters
α | 0.949 + 0.231 i β | -0.169 + 0.133 i γ | 0.169 + 0.133 i δ | 0.949 - 0.231 i
Classical Rodrigues Parameters
q_1 | 0.140 q_2 | 0.178 q_3 | 0.243
Modified Rodrigues Parameters
σ_1 | 0.0683 σ_2 | 0.0866 σ_3 | 0.118