Attitude Dynamics of Rigid Bodies in the Vicinity of the Lagrangian Points
Bibliographic record
Abstract
I N THE last 30 years, several sun-monitoring spacecraft have orbited around the sun–Earth L1 point, and several space observatories will be placed near the sun–EarthL2 in the next decade. Although a large body of literature exists on the orbital dynamics of spacecraft in the restricted three-body problem, very few have explored the attitude dynamics of a rigid Lagrangian-point spacecraft. Kane and Marsh [1] considered the attitude dynamics of an axial symmetric satellite that is rotating about its axis of symmetry, which is normal to the primary bodies’ orbital plane. Robinson [2] first studied the attitude dynamics of a dumbbell satellite located at a triangular point. The same author [3] later determined the equilibrium attitudes of an arbitrary shaped satellite located at a collinear point or at a triangular point and constructed a linear stability diagram about one of the equilibrium configurations. Misra andBellerose [4] studied the librational dynamics of a tethered satellite located at the Earth–moon Lagrangian points and obtained the libration frequencies. The rigid spacecraft is assumed to be held at the Lagrangian points in all of these studies. In practice, however, collinear point satellites are not located directly at the Lagrangian point but in periodic orbits around the point. This note extends the work done by Robinson [3] and Misra and Bellerose [4] and addresses the question of how the translational motions of the spacecraft affect its attitude dynamics. The attitude dynamics of the satellite are studied while it is in a planar Lyapunov orbit and its three-dimensional counterpart. A triangular point spacecraft was previously demonstrated to have two equilibrium configurations, and linear stability diagrams about both equilibrium configurations for a L4 spacecraft are also presented. II. Problem Formulation
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 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".