Bifurcation Graphs for the CR3BP via Symplectic Methods: On the Jupiter–Europa and Saturn–Enceladus Systems
In this article, using the symplectic methods developed by Moreno and Frauenfelder (aimed
at analyzing periodic orbits, their stability and their bifurcations), we will carry out numerical …
at analyzing periodic orbits, their stability and their bifurcations), we will carry out numerical …
The Conley–Zehnder indices of the spatial Hill three-body problem
C Aydin - Celestial Mechanics and Dynamical Astronomy, 2023 - Springer
We explore the interaction between the Conley–Zehnder index and bifurcation points of
symmetric planar as well as spatial periodic orbits in the spatial Hill three-body problem. We …
symmetric planar as well as spatial periodic orbits in the spatial Hill three-body problem. We …
Contact geometry of Hill's approximation in a spatial restricted four-body problem
C Aydin - arXiv preprint arXiv:2407.06927, 2024 - arxiv.org
It is well-known that the planar and spatial circular restricted three-body problem (CR3BP) is
of contact type for all energy values below the first critical value. Burgos-Garc\'ia and Gidea …
of contact type for all energy values below the first critical value. Burgos-Garc\'ia and Gidea …
From Babylonian lunar observations to Floquet multipliers and Conley–Zehnder indices
C Aydin - Journal of Mathematical Physics, 2023 - pubs.aip.org
In 1878, Hill found numerically, in his limiting case of the restricted three-body problem, the
so-called Hill's lunar problem, a planar direct periodic orbit with a period of one synodic …
so-called Hill's lunar problem, a planar direct periodic orbit with a period of one synodic …
Studying network of symmetric periodic orbit families of the Hill problem via symplectic invariants
C Aydin, A Batkhin - arXiv preprint arXiv:2410.21245, 2024 - arxiv.org
In the framework of the spatial circular Hill three-body problem we illustrate the application of
symplectic invariants to analyze the network structure of symmetric periodic orbit families …
symplectic invariants to analyze the network structure of symmetric periodic orbit families …
Symplectic methods in space mission design
Using methods from symplectic geometry, the second and fourth authors have provided
theoretical groundwork and tools aimed at analyzing periodic orbits, their stability and their …
theoretical groundwork and tools aimed at analyzing periodic orbits, their stability and their …
[PDF][PDF] A study of the Hill three-body problem by modern symplectic geometry.
C Aydin - 2023 - researchgate.net
The Hill three-body problem is a limiting case of the restricted three-body problem, which
was first proposed by Hill in 1878. His motivation was to describe the motion of the Moon-the …
was first proposed by Hill in 1878. His motivation was to describe the motion of the Moon-the …