Attitude Determination and Control - AGI

Properties of DCM Rotations
• Determinant of DCM is +1
• DCM rotations are noncommutative (i.e. order
dependent)
• For example, R 321 ≠ R 123.
• DCM are orthnormal (i.e. all columns of matrix A αβ are
linearly independent and form a basis)
• For example, if A αβ =[A 1 ,A 2 ,A 3 ] | A i ∈ R 3 ,
then A i ∙ A j = 0 and A i x A i = A k ∀ i≠j ≠k
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