ON POST-IMPACT ANGULAR VELOCITIES AND RESULTANT IMPULSES WITH RANK-DEFICIENT JACOBIAN MATRICES USING NEWTON IMPACT LAW
Bibliographic record
Abstract
Modeling and trustworthy simulation of impact play an important role in research on robotic contact tasks. Impact dynamic equations, based on Newton impact law, and their solution for planar multi-link robotic collisions have been well developed in literature in the context of determined contact problems. Rank-deficient Jacobian matrices cause the impact equations to be indeterminate. However this issue has not been investigated in previous research. In this paper, the solution for the velocity changes due to impact is proved to be unique in spite of rank-deficient Jacobian matrices and it is solved in a closed form that can be easily employed for simulating robotic system contact states. Furthermore, a set of linear equations with unknown impulses is obtained whereas the impulses can only be solved if extra contact constraints are provided. Two robot collision problems with rank-deficient Jacobian matrices are presented to exemplify the method.
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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".