Optimal Planar Powered Descent with Independent Thrust and Torque
Why this work is in the frame
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Bibliographic record
Abstract
A powered descent problem with a body-fixed thrust vector and independent torque input is considered. By assuming that the entire descent maneuver takes place in an inertially-fixed plane, we show by using the maximum principle that the optimal thrust magnitude must lie on its boundary and may exhibit up to four switches with a min–max–min–max–min profile. The optimal torque input may be singular, and an expression for it is derived. Non-singular torque arcs are shown to be intimately related to the boundary conditions that are imposed on the vehicle’s attitude and the presence of minimum thrust arcs at the beginning and end of the descent. Our results can be thought of as a generalization of previous work on three-degree-of-freedom translational powered descent; with new theoretical insights obtained for powered descent problems that consider attitude in the problem formulation.
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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) | 0.000 | 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