Modal Analysis of the Gyroscopic Continua: Comparison of Continuous and Discretized Models
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Bibliographic record
Abstract
The vibrations of gyroscopic continua may induce complex mode functions. The continuous model governed by partial differential equations (PDEs) as well as the discretized model governed by ordinary differential equations (ODEs) are used in the dynamical study of the gyroscopic continua. The invariant manifold method is employed to derive the complex mode functions of the discretized models, which are compared to the mode functions derived from the continuous model. It is found that the complex mode functions constituted by trial functions of the discretized system yield good agreement with that derived by the continuous system. On the other hand, the modal analysis of discretized system demonstrates the phase difference among the general coordinates presented by trial functions, which reveals the physical explanation of the complex modes.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it