A Unit-Consistent Error Measure for Multibody Systems With Unilateral Constraints
Bibliographic record
Abstract
Modeling multibody systems subject to unilateral contacts and friction efficiently is challenging, and dynamic formulations based on the mixed linear complementarity problem (MLCP) are commonly used for this purpose. The accuracy of the MLCP solution method can be evaluated by determining the error introduced by it. In this paper, we find that commonly used MLCP error measures suffer from unit inconsistency leading to the error lacking any physical meaning. We propose a unit-consistent error measure, which computes energy error components for each constraint dependent on the inverse effective mass and compliance. It is shown by means of a simple example that the unit consistency issue does not occur using this proposed error measure. Simulation results confirm that the error decreases with convergence toward the solution. If a pivoting algorithm does not find a solution of the MLCP due to an iteration limit, e.g., in real-time simulations, choosing the result with the least error can reduce the risk of simulation instabilities and deviation from the reference trajectory.
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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 | 0.005 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 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".