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reference-frame-rotations

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ReferenceFrameRotations.jl for 3D rotation representations (DCM, Quaternion, Euler angles). Use when constructing rotation matrices, converting between rotation representations, composing rotations, or computing attitude kinematics.

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ReferenceFrameRotations.jl

3D rotation representation and conversion library. Repo: JuliaSpace/ReferenceFrameRotations.jl

Types

  • DCM{T} -- 3x3 Direction Cosine Matrix (SMatrix{3,3,T})
  • Quaternion{T} -- Scalar-first: q = q0 + q1·i + q2·j + q3·k
  • EulerAngles{T} -- Three angles (a1, a2, a3) with rotation sequence symbol
  • EulerAngleAxis{T} -- Angle a and axis vector v

Construction

D = angle_to_dcm(θ₁, θ₂, θ₃, :ZYX)          # Euler angles -> DCM
q = angle_to_quat(θ₁, θ₂, θ₃, :ZYX)          # Euler angles -> Quaternion
D = smallangle_to_dcm(δx, δy, δz)             # Small angle approximation
q = Quaternion(1.0, 0.0, 0.0, 0.0)            # Identity quaternion
D = DCM(I)                                     # Identity DCM

12 rotation sequences: :XYX, :XYZ, :XZX, :XZY, :YXY, :YXZ, :YZX, :YZY, :ZXY, :ZXZ, :ZYX, :ZYZ

Conversions (bidirectional between all types)

q = dcm_to_quat(D)              D = quat_to_dcm(q)
ea = dcm_to_angle(D, :ZYX)      D = angle_to_dcm(ea)
aa = dcm_to_angleaxis(D)        D = angleaxis_to_dcm(aa)
ea = quat_to_angle(q, :ZYX)     q = angle_to_quat(ea)

Composition

D3 = compose_rotation(D1, D2)        # Same type required
D3 = D2 ∘ D1                         # Mixed types OK (converts to left type)
q3 = q1 * q2                         # Hamilton product

Kinematics

dq = dquat(q_ba, ω_ba_b)    # Quaternion time-derivative from angular velocity
dD = ddcm(D_ba, ω_ba_b)     # DCM time-derivative from angular velocity

Utilities

inv_rotation(D)        # Inverse rotation (transpose for DCM)
orthonormalize(D)      # Gram-Schmidt re-orthonormalization
conj(q)                # Quaternion conjugate
norm(q)                # Quaternion norm

Key Conventions

  • Quaternion scalar-first convention: (q0, q1, q2, q3)
  • All angles in radians
  • All types immutable, backed by StaticArrays
  • AD support via ForwardDiff/Zygote extension