Direct method for deriving equilibrium equations in solid continuous systems
Bibliographic record
Abstract
In this paper, a simplified method is proposed for deriving equilibrium equations in continuous systems. The new method is indeed the direct applying of Newton's laws on free body diagram of point. First, by describing the concept of equilibrium equations and investigating the differences between concentrated masses and continuous systems, the physical basis of new method is introduced. It is shown that, using intensive properties simplifies the analysis of continuous systems. For verifying the new method, the governing equations in Cartesian, polar and spherical coordinates systems are derived. We have to consider nonlinear terms due to developing large slopes in system. Hence, nonlinear governing equations in Cartesian system are derived too. Finally by noting to the simplicity of new method and its independency from complicated differential and vector analysis in other methods such as Hamiltonian and classic methods, the interests of new method are emphasized. By knowing concept of physical point, a united process is accessible which is extendable to other governing equations of continuous systems.
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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 | 0.001 | 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".