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Is Reference Frame Rotations free to use?

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Who published Reference Frame Rotations?

majiayu000 (@majiayu000) published this skill. Their other Agent Skills are listed on their SkillMD profile.

Reference Frame Rotations by majiayu000

Name: Reference Frame Rotations
Rating: 4.2 (5 reviews)
Author: majiayu000

Reference Frame Rotations

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.

majiayu000 7207883 2 files · 3.3 KB Updated Sep 9, 2026 567 repo stars

File contents

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

---name: reference-frame-rotationsdescription: 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.--- # ReferenceFrameRotations.jl 3D rotation representation and conversion library. Repo: [JuliaSpace/ReferenceFrameRotations.jl](https://github.com/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 ```julia 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) ```julia 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 ```julia D3 = compose_rotation(D1, D2) # Same type required D3 = D2 ∘ D1 # Mixed types OK (converts to left type) q3 = q1 * q2 # Hamilton product ``` ## Kinematics ```julia 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 ```julia 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

Frequently asked questions