Coordinate systems, origins & datums

This page records the frames, orderings, and reference points VANE assumes, so that results can be interpreted unambiguously.

Reference frames

Rotating (blade) frame

The frame OpenFAST writes for blade degrees of freedom, rotating with the rotor. Channels carry a per-channel rotating-frame flag in the .lin tables; this is the hook the MBC3 transform uses to find blade triplets.

Non-rotating (fixed) frame

The frame after the MBC3 transform. The three per-blade coordinates of a triplet become a non-rotating [collective, cosine, sine] set. The averaged model lives entirely in this frame; tower, drivetrain, and platform degrees of freedom are already non-rotating and pass through unchanged.

Azimuth convention

Rotor azimuth is read from the .lin header in radians and wrapped to [0, 360) degrees internally for sweep-coherence checks. The MBC3 transform integrates over a full revolution; the averaged model is independent of the azimuth origin for an isotropic rotor.

State-space layout

After the transform, the state vector is reordered into the canonical block layout

x = [ q2 ; q2dot ; q1 ]

where q2 are the second-order (displacement) degrees of freedom, q2dot their time derivatives, and q1 the first-order states. Mode shapes are reported over the displacement block (q2); the eigensolver reduces the full eigenvectors to those rows. Multi-blade coordinate annotations (MBCResult.mbc_coordinates → ModalSolution.dof_mbc_coordinates) record, for each state, whether it is a collective, cosine, or sine coordinate.

Degree-of-freedom mapping

Each channel description embeds an OpenFAST internal DOF token (for example DOF_TFA1 for the first tower fore-aft mode or DOF_BF(1,1) for blade 1’s first flapwise mode). classify_dof() maps that token onto a physical DOF category, originating module, and blade index, which drives labelling and the blade collective/regressive/progressive taxonomy.

Origins and datums

VANE does not re-define geometric origins; it inherits OpenFAST’s. Rotor/tower geometry extracted from the ElastoDyn input (hub height, tower stations, blade length) is reported in the model’s own datum for context only and is not used to re-reference the state-space model.