BeamDyn: rotating-frame-consistent linearization Jacobians when RotStates=True

[mayankchetan]

Feature or improvement description

Fixes #3394. With RotStates = True (the default), the BeamDyn linearization Jacobians are a
frozen, root-aligned snapshot in the inertial frame. But the .lin rows and columns are
flagged RotatingFrame = T. MBC3-based postprocessors thus inject spurious spin-softening
(f² = f₀² − αΩ²) into speed-independent branches. Example: the 5-MW tower side-side branch
droops 2.29 % at 12 rpm, and the IEA-22 droops ~8 % at rated speed.

This PR makes the returned Jacobians frame-consistent with the flag. A new subroutine
BD_JacRotFrame in modules/beamdyn/src/BeamDyn.f90 applies, per paired (q, dq/dt) state
triplet (pairing offset Nx/2):

A_r = S·A·S⁻¹ + blkdiag(−ω̃)     with  S = [[I, 0], [−ω̃, I]]
B_r = S·B,   C_r = C·S⁻¹

to dXdx / dXdu / dYdx. Here ω is the full root RotationVel 3-vector, mapped into the
frozen GlbRot basis. A scalar Ω is not sufficient: precone alone puts −0.0548 rad/s in z at
12 rpm on the 5-MW. At standstill the transform is exactly the identity. This is not a
revert of the PR #2063 code that 5fbd380f8 removed. That code was ≈identity at the operating
point, and it lacked the transport (Coriolis) term. It therefore never produced rotating-frame
Jacobians.

Design choice — where the transform lives. A new optional IsLin flag gates the
transform. The flag is threaded ModGlue_Linearize → FAST_JacobianPInput / FAST_JacobianPContState (FAST_Funcs.f90) → BD. The transform thus applies only at
linearization snapshots. The tight-coupling solver (BuildJacobianTC) and the AeroMap calls
are unflagged. They keep the raw frozen-frame Jacobians that their Newton iterations require.
All existing callers use keyword arguments. No C-binding, Simulink, or module-driver
interfaces are affected. No registry regeneration is needed. An alternative placement is also
workable: apply the transform glue-side in FAST_ModGlue.f90 and keep the module API
flag-free. We are glad to rework to that form if the maintainers prefer it.

Runtime guards: fatal on a state-layout-invariant violation, and fatal on a gross
re-anchoring deviation (>1e-3). The code warns once per snapshot on a measurable re-anchoring
deviation (>1e-6), on ω̇ ≠ 0, and on |WM parameters| > 0.2 (the first-order
rotation-composition limit).

Known limitation (documented in #3394): floating platforms. Platform and yaw rates fold into
the root ω. There, the scalar-Ω assumption of MBC3 independently breaks down.

Related issue, if one exists

Fixes #3394. Companion defect: #3395, fixed by PR #3393 (the .lin full-precision writer).
That defect is independent, and it also corrupts BD Campbell work. The two PRs are
independent, but one investigation isolated both. The verification input files here
neutralize #3395 with OutFmt "ES18.9E3".

Impacted areas of the software

• modules/beamdyn/src/BeamDyn.f90 — new BD_JacRotFrame, applied in BD_JacobianPInput /
  BD_JacobianPContState when p%RotStates .and. IsLin. The dead RotateStates
  declarations are removed.
• modules/openfast-library/src/FAST_Funcs.f90, FAST_ModGlue.f90 — these thread the
  optional IsLin flag from ModGlue_Linearize only.
• Time marching is byte-identical code. Standstill linearization output is bit-identical.

Additional supporting information

This branch is based on rc-5.0.1 to target the upcoming patch release (rebased 2026-07-21
from dev @ 0160d29a0; the three changed files are identical in both bases).
The acceptance gate was re-run on an rc-5.0.1 build of this branch and passes: tower-SS
flatness 0.015 % over 0–12 rpm, all damping ratios positive.

Verification (double precision, dev @ 0160d29a0, wide-format input files):

• NREL 5-MW Campbell 0–25 rpm (CompElast=2): the tower-SS flatness improves from 2.29 %
  to 0.015 %. The patched results match an independent python-side transform of the
  unpatched matrices to ≤0.02 %. They match the ElastoDyn reference to ≤0.6 %. All damping
  ratios are positive.
• IEA fleet (29 cases; IEA-15/3.4/10/22 ported to dev): patched Fortran vs the python
  reference agrees to ≤0.022 % per point. The SS flatness is 0.111 % / 0.029 % / 0.026 % /
  0.379 %. The IEA-22 residual equals the python reference's own 0.361 % (a second-order
  WM/prebend effect, not introduced here). The raw unpatched droop there is ~8 %.
• Standstill: the .lin numbers are bit-identical, patched vs unpatched
  (timestamp-only diff).
• ω mapping: an instrumented print reproduced the per-blade target vector, with the
  −2.5° precone z-component included (the instrumentation is removed).

Generative AI usage

Developed with Anthropic Claude (Claude Code) under human direction. The whole branch was
independently reviewed before submission.

Co-authored-by: Anthropic Claude claude@anthropic.com

Test results, if applicable

• r-test branch merging required

r-test impact: the baselines change for 5MW_Land_BD_Linear, 5MW_Land_BD_Linear_Aero, and
Damped_Beam_Rotating. This change is the fix at work: the rotating-case Jacobians change by
design. Damped_Beam_Rotating runs clean on the patched binary. The standstill beam cases
are identical. All CompElast = 1 cases are unaffected. The companion r-test branch
(17 regenerated .lin baselines) is prepared on the same branch name and is rebased onto
r-test rc-5.0.1. This PR stays a draft until that branch is opened as an r-test PR. We
can regenerate baselines on request, or follow the maintainer process.

[mayankchetan]

Follow-up commit f230c16a4 from an additional adversarial review pass on the branch: two guard-ordering edge cases in BD_JacRotFrame (no change to the transform itself).

1. The standstill early-return now precedes the re-anchoring invariant guard — at ω = 0 every operation is an exact identity regardless of frame alignment, so the routine returns the Jacobian unchanged instead of potentially aborting on a mis-anchored root. This makes the advertised standstill no-op unconditional.
2. The zero-speed path no longer returns silently when the root is accelerating (ω = 0, ω̇ ≠ 0, e.g. a LinTimes snapshot during startup): it now emits the same omitted-ω̇-transport-term warning as the spinning path before returning.

Re-verified after the change: the 7-speed 5-MW acceptance checker passes with identical numbers (tower-SS flatness 0.015 %).