2006.14844
Lagrangian dynamics by nonlocal constants of motion
Gianluca Gorni, Gaetano Zampieri
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves finite-time past blow-up for mq̈ = −k|q̇|q̇ − ∇U with 0 ≤ U ≤ Usup when the initial kinetic energy exceeds Usup, using a nonlocal constant of motion and a comparison ODE; the candidate independently derives the same result via a short, direct energy/Osgood argument. Hypotheses and conclusions match; both arguments are logically sound.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper’s main new application (finite-time past explosion under quadratic drag and bounded potential) is correct and clearly presented. It meaningfully showcases the nonlocal constant-of-motion method. Including a brief alternative energy-based derivation would improve accessibility and underscore the sharp threshold without auxiliary parameters.