Non-Linear Stability of L 4 in the Restricted Three-Body Problem When the Smaller Primary is a Finite Straight Segment Under Resonance Cases
Bibliographic record
Abstract
In this paper, we have studied the non-linear stability of the triangular libration point L4 in the restricted three-body problem when the smaller primary is a finite straight segment of length 2l under the presence of third and fourth order resonances. It is well known that most of the asteroids are irregularly shaped elongated bodies. We have taken these elongated bodies as a finite straight segment. We have used Markeev's theorem (1978) [1] to examine the non-linear stability for resonance cases 2:1 and 3:1. We have found that the triangular equilibrium solutions are always unstable in the third and fourth order resonance cases for 0 ≤ l < 0.05. We have applied the results to the following solar systems (i) Jupiter - 9 Metis (ii) Jupiter - 22 Kalliope (iii) Jupiter - 216 Kleopatra (iv) Jupiter 243 Ida (v) Jupiter - 433 Eros (vi) Jupiter - 951 Gaspra.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".