Geometric mechanics framework for tethered de-spinning of massive asteroids by small tug using passivity-based control
Bibliographic record
Abstract
This paper develops a geometric mechanics framework for de-spinning massive asteroids using miniature tethered tugs during the post-capture phase of asteroid redirection missions. The excessive mass disparity between the asteroids and the tug, combined with weak solar gravity in heliocentric orbits at several astronomical units from the Sun, renders the tug-asteroid system severely ill-conditioned. This condition poses challenges for accurately integrating the de-spinning dynamics numerically over extreme long durations. To address these issues, this paper derives the relative equations of motion of the tug-asteroid system via Hamilton’s principle and Lie group theory within a structure-preserving methodology that incorporates tether libration and asteroid attitude dynamics. The asteroid de-spinning control scheme is synthesized through energy shaping to establish system passivity via tether tension control to ensure bounded stability. A discrete-time Lie group Hamiltonian variational integrator is derived based on the Symplectic Partitioned Runge-Kutta method for high accuracy. The strict asymptotic stability of the proposed passivity-based control is proved theoretically. The framework is applied to de-spin asteroids at 1 and 3 astronomical units from the Sun. Numerical results demonstrate enhanced stability over extremely long time integration, which is critical for such missions. Finally, the impact of variations in asteroid’s moment of inertia and initial conditions is analyzed parametrically, revealing that small changes can significantly affect mission duration and the required tether length.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".