GYRO-01…06 check zero-speed recovery, disk identities, an independent oscillator oracle, signed-speed splitting, tracking, and an internal BEAM2 refinement series.
01 Model and scope
The 0.2.11 records check separate stages: recovery at zero speed, disk matrix identities, an independent analytical oscillator, signed-speed splitting, mode-tracking behaviour and an internal mesh sequence. Passing these checks bounds numerical evidence for the declared rotor model; the ambiguous high-frequency branch remains visible.
Route assumptions and calculation checks
- Frequency delta and residual meet the frozen numerical thresholds for this model.
- The high-frequency pair remains ambiguous at 100 rad/s; tracking preserves that ambiguity.
- This is internal mesh-convergence evidence, not physical validation or critical-speed validation.
Useful foundations and prerequisites
02 Essential equations and symbols
Definitions and conventions
- GYRO-01…06
- Named verification records in the v0.2.11 summary.
- Prescribed signed spin speed.
- QEP residual
- Residual of the quadratic eigenvalue pencil.
- MAC
- Mode-shape correlation used in branch tracking.
03 Step by step derivation
Follow the assumptions, equations and discrete operations in order. The full explanation stays visible.
1 · Verify independent parts of the rotating route
The GYRO-01…06 records test zero-speed recovery to classical modes, rigid-disk matrix identities, an independent oscillator oracle, signed-speed splitting, mode tracking, and an internal BEAM2 mesh series. Each check targets a different source of error in the rotating pencil.
2 · Read signed-speed and tracking observations
The frozen speeds are Ω=0, 100, and 250 rad/s, with 4/8/16/32 BEAM2 refinement levels. A gyroscopic term can split forward/backward branches as spin changes. The high-frequency pair remains ambiguous at 100 rad/s, and the plot deliberately preserves that unresolved lineage.
3 · Bound the engineering conclusion
The reported frequency delta and residual meet the frozen numerical thresholds for this specific model. Internal mesh convergence is not physical validation, bearing validation, operating-risk assessment, or critical-speed certification. Both rotor routes remain experimental and inherit their explicit modeling restrictions.
04 Algorithm and implementation
This sheet provides explanatory references rather than an inline source excerpt. Use the labeled sources to inspect the precise boundary.
05 Verification and limitations
EXPERIMENTAL · internal mesh convergence
Each reference supports its own model, observable and analysis route. Read the original contract and limitations before transferring a conclusion.