A method to enforce stiff constraints in the simulation of articulated multibody systems
Bibliographic record
Abstract
We propose a novel integrator for implementing bilateral constraints in multibody simulation using variational integrator methods. We first construct a variational penalty method, which is used to enforce a constraint. The penalty term is simulated using an asynchronous variational integrator, allowing the penalty part of the system to be simulated using a smaller time step. We compute the Discrete Euler-Lagrange (DEL) equations for an equivalent penalty term with a larger time step and then use this rescaled system in the aforementioned variational penalty method, thereby enforcing the constraints. This enables us to incorporate some of the behavior of a very stiff system, which would only be stable on the small time scale, into the system on the large time scale. The effect is better adherence to the constraints, at a larger time step. We demonstrate the method with a simulation of a chain of rigid bodies. We then discuss the potential applications of the integrator and highlight how the work can be used to better interpret the tuned values of the coefficients used in penalty formulations.
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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) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 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".