Galerkin Variational Integrators for Orbit Propagation with Applications to Small Bodies
Bibliographic record
Abstract
The development of fixed-step higher-order variational integrators based on geometric integration methods is presented. These methods are symplectic, preserve energy in Hamiltonian conservative systems, and are highly accurate for long-term integration. By properly selecting a quadrature rule and control points in the polynomial approximation of the trajectory, a fast algorithm that reduces the number of computations of the gravitational force terms is constructed. Numerical simulations are presented for different scenarios, comparing Galerkin variational integrators against traditional fixed-step propagators used in astrodynamics applications. An error analysis is then performed, focusing on the implications of energy conservation and the accuracy of the methods. It is found that, under certain conditions, Galerkin methods are superior to nonsymplectic integrators for long-term orbital propagation, reducing simulation times significantly for long integration periods. This makes the methods suitable for long-term orbital dynamics applications about small bodies, such as asteroids.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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".