Step 2: finite-rotation-state

읽어야 할 파일

AGENTS.md
docs/ARCHITECTURE.md
docs/ADR.md
docs/nonlinear-static-newton-raphson/formulation.md
docs/nonlinear-static-newton-raphson/numerical-review.md
docs/nonlinear-static-newton-raphson/implementation-plan.md
include/fesa/math/vector3.h
include/fesa/math/matrix.h
tests/unit/math/vector3_test.cpp
tests/unit/math/matrix_test.cpp
Step 1 files: include/fesa/model/model_types.h, include/fesa/model/domain.h

이전 Step 전제

Step 1 exposes nonlinear static semantic selection. This Step adds finite rotation math used by nonlinear MITC4 and state recovery.

소유 파일

Create: include/fesa/elements/finite_rotation.h
Create: src/fesa/elements/finite_rotation.cpp
Create: tests/unit/elements/finite_rotation_test.cpp
Modify: src/fesa/CMakeLists.txt
Modify: tests/CMakeLists.txt

인터페이스

namespace fesa {

struct FiniteRotationState {
  Vector3 phi;
  Matrix q;
  Vector3 director;
};

Matrix ExpSkew(const Vector3& phi);
Matrix LeftJacobianSO3(const Vector3& phi);
Matrix InverseTransposeLeftJacobianSO3(const Vector3& phi);
Result<FiniteRotationState> MakeFiniteRotationState(
    const Vector3& phi, const Matrix& initial_frame);
Result<FiniteRotationState> ApplyGlobalRotationIncrement(
    const FiniteRotationState& committed,
    const Vector3& delta_phi,
    const Matrix& initial_frame);

}  // namespace fesa

RED

Add tests first.

NSNR-ROT-001: zero phi returns Q0 and director=Q0*e3.
NSNR-ROT-002: finite phi satisfies Q=exp(phi^)Q0, Q^T Q=I, det(Q)=1, director=Qe3.
NSNR-ROT-003: update uses Q+ = exp((phi + delta_phi)^)Q0.
NSNR-ROT-004: principal branch margin sqrt(epsilon_double) rejects ambiguous rotations near pi.
NSNR-ROT-005: LeftJacobianSO3 and inverse-transpose are finite and derivative-consistent for small, medium, and near-branch-safe rotations.
NSNR-ROT-006: nonfinite rotation components fail with invalid-accepted-state or the Step-introduced finite-rotation diagnostic.

Run:

cmake --build .harness/build --config Debug
ctest --test-dir .harness/build -C Debug -R "FiniteRotation" --output-on-failure

Expected: tests fail because the rotation module does not exist. Unexpected pass stops.

GREEN

Implement the SO(3) helper functions with finite checks and principal-branch validation. Use existing FESA math types and keep MKL/vendor types out of public headers.

VERIFY

cmake --fresh -S . -B .harness/build -G "Visual Studio 18 2026" -A x64 `
  "-DFESA_GTEST_SOURCE_DIR=$gtestSource" `
  "-DMKL_DIR=$mklDir" `
  "-DTBB_DIR=$tbbDir" `
  "-DHDF5_DIR=$hdf5Dir"
cmake --build .harness/build --config Debug
ctest --test-dir .harness/build -C Debug -R "FiniteRotation" --output-on-failure
ctest --test-dir .harness/build -C Debug --show-only=json-v1
ctest --test-dir .harness/build -C Debug --output-on-failure

Recheck .harness/config.json before using default commands.

상태 기록

Update only Step 2 status and summary/error/blocked payload. Executor owns timestamps, commits, retry, and advancement.

금지사항

Do not normalize invalid rotation matrices to make tests pass. 이유: invalid nonlinear state must fail closed.
Do not add element residual or tangent code here. 이유: this Step owns only finite rotation state.
Do not expose backend/vendor types. 이유: public solver core must remain backend-neutral.

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