Inclusion of Non-Conservative Forces in Geometric Integrators with Application to Orbit–Attitude Coupling
Bibliographic record
Abstract
In this paper, a discretization method for incorporating nonconservative forces in a class of geometric numerical integrators known as variational integrators and Galerkin variational propagators is proposed. The proposed method does not require modification of the original integration algorithm used in conservative systems. First, the damped harmonic oscillator is used as benchmark for evaluating the proposed approach. Two more complex scenarios are presented next: one considering propagations in the two-body problem with drag forces, and another dealing with long-term translational propagations about small bodies considering orbit–attitude coupled force terms where the attitude is prescribed. Numerical experiments are performed, comparing results to a nominal analytical solution when it is available, or against a highly accurate propagated reference trajectory. The results in this paper show that including the nonconservative forces in the potential energy term for the discrete equations produces a very accurate discretization. This allows one to perform accurate and fast long-term numerical propagations with structure preserving variational algorithms, in scenarios where perturbations to the system can be modeled as nonconservative forces.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 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) | 0.001 | 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".