General Dynamics in the Restricted Full Three-Body Problem
Bibliographic record
Abstract
Abstract The problem of a binary system and a spacecraft in its gravity field is studied. As the mass distribution of the bodies is considered, the two problems are referred as the Full Two Body Problem (F2BP) and the Restricted Full Three Body Problem (RF3BP), respectively. The conditions for relative equilibria and their stability in the F2BP were derived for an ellipsoid–sphere system. As the non-equilibrium problem is more common in nature, we look at periodic orbits in the F2BP close to the relative equilibrium conditions. It is found that families of periodic orbits can be computed where the minimum energy state of one family is the relative equilibrium state. An approximation method was derived in order to facilitate the computation of periodic orbits near relative equilibria while keeping the interesting dynamical features. The next step is to make the connection between the dynamics of the RF3BP and the F2BP. In the current paper, we solve for the dynamics of the F2BP and substitute this model in the RF3BP. We provide a basic investigation of the dynamics of a particle in the gravitational field of this binary system. We show results in the F2BP and the RF3BP.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 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".