On derivation of constrained multiple rigid body dynamic equations
Bibliographic record
Abstract
Dynamic modeling of constrained multi-link systems are traditionally tackled either in the reduced state space or in the non-reduced state space. In this paper, an alternative approach for deriving dynamic equations for a class of multi-link constrained systems is proposed. The constraints, studied in this paper, are joints where the constraint forces are of interest. The method starts with replacing the joints with virtual links. Next, the augmented state space is formed by the states describing the original physical system and virtual links. The dynamic equations, describing the expanded systems, are then derived in the reduced state space from the viewpoint of the augmented state space. Finally, the dynamic equations for the original multi-link systems are obtained by setting all the physical parameters and states associated with virtual links to zero. This alternative approach has the advantages of both traditional methods in that: (i) the constraint forces can be determined directly, (ii) the violation of constraints is avoided, which is the main problem for dynamic modeling of constrained systems in the non-reduced state space, and (iii) all computer software packages for automatic generation of dynamic equations in the reduced state space can be readily used.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
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".