Self Recovery Phenomenon of Mechanical Systems With Unactuated Cyclic Variables due to Damping-Like Forces
Bibliographic record
Abstract
The conservation of momentum can be useful in designing control laws for underactuated mechanical systems. However, the momentum is conserved only for unactuated variables with symmetry. If a symmetry-breaking force is applied to a system, the momentum is not conserved any longer in general. The main objective of this paper is to show that there exist forces linear in velocity such as the damping force that break the symmetry but induce a new conserved quantity in place of the original momentum map. This paper formalizes that such a new conserved quantity can be constructed by combining the time integral of a general damping force and the original momentum map associated with the symmetry. Especially, we show that the new conserved quantity can exist for multiple variables with symmetry. From the perspective of stability theories, the major implication of the new conserved quantity is that the corresponding variables possess the self recovery phenomenon, i.e. they will be globally attractive to the initial condition of the variables. What is fundamental in the damping-induced self recovery is not the positivity of the damping coefficient but certain properties of the time integral of the damping force. Self recovery effect and theoretical findings are demonstrated by simulation results using a two-link manipulator and a planar pendulum. The results in this paper will be useful in designing and controlling mechanical systems with underactuation.Copyright © 2012 by ASME
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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".