DYNAMICS OF AN ISOSCELES PROBLEM GENERATED BY A PERTURBATION OF EULER’S COLLINEAR SOLUTION

Karine de Almeida Santos

correctmedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves (i) the circle of equilibria, (ii) the ε=0 linearization spectrum p(λ) = −λ^2((2μ+1)/κ + λ^2)(λ^2+1), and (iii) the reduction via the cyclic angle giving the 2–d.o.f. Hamiltonian with conserved v2=γ and the uniqueness of the reduced equilibrium P* when γ=1. The candidate solution reproduces these steps with essentially the same constructions, formulas, and conclusions. Minor issues are purely presentational: a notational shift in the polar change (x1 versus 1+x1) and one unnecessary sign argument in forcing x3=0 (the paper’s “for all ν” argument is cleaner).

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The work correctly identifies the circle of equilibria, derives the unperturbed spectrum, and executes a clean symplectic reduction using the first integral. Results align with standard methods and are internally consistent. Minor derivational details (e.g., uniqueness of the reduced equilibrium) are stated without proof and can be added succinctly. Clarifying notational choices (especially the shift by 1 in the polar change) would improve readability.