Dynamics representation of mechanical systems for time-stepping problems
Bibliographic record
Abstract
This paper introduces a novel two-stage time-stepping framework for mechanical systems. The method separates the update of configuration and dynamics: configuration is advanced using independent (joint) velocities, while the dynamic equations are formulated using a dependent set of velocities—specifically, the velocity of body-fixed points and the angular velocity of each rigid body. These dependent velocities are projected onto the joint space to ensure that kinematic constraints are satisfied at the position level, eliminating the need for constraint stabilization techniques. A key advantage of this decomposition is that it enables a compact and transparent expression of the nonlinear inertial terms, which can then be integrated either explicitly or implicitly within the same framework. This flexibility makes the approach particularly well suited for time-stepping schemes, including those used in challenging scenarios such as unilateral contact problems. Numerical results illustrate how different integration strategies and velocity representations affect the stability and accuracy of the solution, highlighting the robustness of the proposed method. • New formulation for time stepping. • Separation of dynamics (impulse–momentum), and kinematics (velocity–position) steps. • Constraints are satisfied without stabilization techniques. • Detailed analysis of nonlinear inertial terms in explicit and implicit time stepping. • Well suited for the development of stable time-stepping methods in 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 | 0.001 |
| 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".