2104.02432
JACOBI STABILITY ANALYSIS OF THE CLASSICAL RESTRICTED THREE BODY PROBLEM
Cristina Blaga, Paul A. Blaga, Tiberiu Harko
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper derives the KCC deviation tensor for the CR3BP as P^i_j = U_{x^i x^j} + ε_{iℓ} ε^ℓ{}_j, yielding components P11=U_xx−1, P22=U_yy−1, P12=U_xy, and shows that at L4,L5 the eigenvalues are λ± = 1/2 ± (3/4)√(1+3(1−2μ2)^2), while at L1–L3 they are real with opposite signs; hence all five Lagrange points are Jacobi unstable . The candidate solution reproduces this same reduction P = Hess(U) − I, evaluates it at L4,L5 and the collinear points using the standard CR3BP potential and coordinates, and reaches the identical conclusion. The steps, formulas, and conclusions match the paper’s derivation and final claim that all Lagrange points are Jacobi unstable .
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper correctly applies KCC/Jacobi stability analysis to the CR3BP and clearly demonstrates that all five Lagrange points are Jacobi unstable, contrasting this with classical Lyapunov stability. The derivations are sound and the main theorem is supported by explicit computations at each equilibrium. Minor clarifications on conventions and assumptions would further enhance clarity.