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Szumiński, Wojciech, 2024, "Source data for: Non-integrability of the planar elliptic restricted three-body problem", https://doi.org/10.18150/9WJFDY, RepOD, V1
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We study the integrability of 2D Hamiltonian systems $H_\mu=\frac{1}{2}(p_1^2+p_2^2) + \omega(p_1q_2-p_2q_1) -\tfrac{\mu}{r}+ V(q_1,q_2)$, where $r^2=q_1^2+q_2^2$, and potential $V(q_1,q_2)$ is a homogeneous rational function of integer degree $k$. The main result states that under very general assumptions: $\mu\omega\neq0$, $|k|>2$ and $V(1,\rmi)\neq 0$ or $V(-1,\rmi)\neq 0$, the system is not integrable. It was obtained by combining the Levi--Civita regularization, differential Galois methods and the so-called coupling constant metamorphosis transformation.The proof that the regularized version of the problem is not integrable contains the most important theoretical results, which can be applied to study integrability of other problems.
The Hill problem · Integrability obstructions · Super-integrability · Regularisation
Przybylska, M., Maciejewski, A.J. Integrability of Hamiltonian systems with gyroscopic term. Nonlinear Dyn 111, 275–287 (2023). https://doi.org/10.1007/s11071-022-07866-w doi: https://doi.org/10.1007/s11071-022-07866-w
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