2011.03330
Safe trajectory of a piece moved by a robot
Ernest Benedito, Oliver Bond, Thomas Babb, Juan R. Pacha, Sandeep Kumar, Joan Solà-Morales
correctmedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper reduces the rod model to λ wₓₓₓₓ = θ̇² w with clamped–free boundary conditions and states, without derivation, that nontrivial solutions occur iff cosh β cos β + 1 = 0 for β = (θ̇²/λ)^{1/4} . The candidate solution supplies the missing algebra via the standard determinant calculation for the clamped–free Euler–Bernoulli beam, reaching exactly the same dispersion relation and a matching eigenfunction form. Aside from a small typographical glitch in the paper’s displayed mode shape (cos(βn) instead of cos β), the results coincide.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The simple rod eigenproblem is correctly reduced and the stated eigenvalue condition is classical and accurate. The omission of the short determinant calculation and a small typographical error in the mode shape are the only issues. The result is sound and useful in the paper’s broader context.