A new formulation for the dynamics of rigid bodies with unilateral interactions
Bibliographic record
Abstract
A new approach is introduced for modelling multibody systems with unilateral interactions. We focus on the simulation of the forward dynamics problem. The dynamic and kinematic steps are solved with two different formulations. First, a four-point-mass model is used to represent the rigid body dynamics, avoiding the use of rotational coordinates. Therefore, the nonlinear inertial terms do not appear explicitly in the formulation. However, there are constant distance constraints between the point masses. The velocities of the point masses are obtained by solving the dynamics with this model. The angular velocity of the rigid body can be calculated from such velocities. Then, the kinematic problem is solved using the rigid body representation that fully embeds the constant distance constraints. Thus, the proposed approach can improve the accuracy of the dynamic problem with unilateral contact since the nonlinear inertial terms do not enter the formulation explicitly. The constraints appear explicitly in the dynamics representation, but they are linear there. In the position update, they are embedded exactly through the model change back to the angular velocity-based minimum coordinate formulation.
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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".