A Friction Model for Non-Singular Complementarity Formulations for Multibody Systems With Contacts
Bibliographic record
Abstract
The dynamics of multibody systems with many contacts are frequently formulated as a Linear Complementarity Problem (LCP), for which several direct or iterative algorithms are available to solve it efficiently. These formulations rely on discretized friction models that approximate the friction cone of the Coulomb model to a pyramid. However, they produce rank-deficient LCPs even though the physical problem does not have constraint redundancy and has a unique solution. Here, a new discretized friction model is presented which results in an LCP formulation with a full-rank lead matrix. This model relies on an inertial term to couple the equations of the model, which behaves as close to the Coulomb model as the other discretized models. Moreover, it is shown through some simulations that some algorithms can be used with this formulation, which could not be used with the other rank-deficient LCP formulations.
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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".