A new understanding of L4 and L5 axial orbits through the torus structure
Bibliographic record
Abstract
ABSTRACT In this paper, through the critical isosurface of the pseudo-Hamiltonian of co-orbital motions in the torus space, we provide a new understanding of L4 and L5 axial orbits and their invariant manifolds in the circular restricted three-body problem. The contact points on the critical isosurface of the pseudo-Hamiltonian correspond to the locations of L4 and L5 axial orbits in the torus space, and provide a set of good initial guesses of L4 and L5 axial orbits for the multiple shooting method. Furthermore, we calculate and analyse orbital behaviours of L4 and L5 axial orbit families. Based on the topological structure of the critical isosurface of the pseudo-Hamiltonian, compound dynamical motions of invariant manifolds associated with L4 and L5 axial orbits are discussed. We present an approximate estimation for libration amplitudes of different co-orbital portions of invariant manifolds. Results obtained from numerical integration demonstrate the validity of our semi-analytical approach in the torus space..
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".