arXiv subjects

Dayung Koh

Publications and source records attributed to Dayung Koh.

3 recordsLinked to original sources

arXiv2025

Bifurcations of highly inclined near halo orbits using Moser regularization

We study the bifurcation structure of highly inclined near halo orbits with close approaches to the light primary, in the circular restricted three-body problem (CR3BP). Using a Hamiltonian formulation together with Moser regularization, we develop a numerical framework for the continuation of periodic orbits and the computation of their Floquet multipliers which remains effective near collision. We describe vertical collision orbits and families emerging from its pitchfork, period-doubling, and period-tripling bifurcations in the limiting Hill's problem, including the halo and butterfly families. We continue these into the CR3BP using a perturbative framework via a symplectic scaling, and construct bifurcation graphs for representative systems (Saturn-Enceladus, Earth-Moon, Copenhagen) to identify common dynamical features. Conley-Zehnder indices are computed to classify the resulting families. Together, these results provide a coherent global picture of polar orbit architecture near the light primary, offering groundwork for future mission design, such as Enceladus plume sampling missions.

math.DS↗

arXiv2024

Symplectic geometry and space mission design

Using methods from symplectic geometry, the second and fifth authors have provided theoretical groundwork and tools aimed at analyzing periodic orbits, their stability and their bifurcations in families, for the purpose of space mission design. The Broucke stability diagram was refined, and the "Floer numerical invariants" where considered, as numbers which stay invariant before and after a bifurcation, and therefore serve as tests for the algorithms used. These tools were later employed for numerical studies. In this article, we will further illustrate these methods with numerical studies of families of orbits for the Jupiter-Europa and Saturn-Enceladus systems, with emphasis on planar-to-spatial bifurcations, from deformation of the families in Hill's lunar problem studied by the first author. We will also provide an algorithm for the numerical computation of Conley--Zehnder indices, which are instrumental in practice for determining which families of orbits connect to which. As an application, we use our tools to study a family of periodic orbits that approaches Enceladus at an altitude of 29km, and therefore may be used in future space missions to visit the water plumes.

math.SG↗

arXiv2023

Symplectic methods in the numerical search of orbits in real-life planetary systems

The intention of this article is to illustrate the use of methods from symplectic geometry for practical purposes. Our intended audience is scientists interested in orbits of Hamiltonian systems (e.g. the three-body problem). The main directions pursued in this article are: (1) given two periodic orbits, decide when they can be connected by a regular family; (2) use numerical invariants from Floer theory which help predict the existence of orbits in the presence of a bifurcation; (3) attach a sign +/- to each elliptic or hyperbolic Floquet multiplier of a closed symmetric orbit, generalizing the classical Krein--Moser sign to also include the hyperbolic case; and (4) do all of the above in a visual, easily implementable and resource-efficient way. The mathematical framework is provided by the first and third authors, where the ``Broucke stability diagram'' was rediscovered, but further refined with the above signs, and algebraically reformulated in terms of GIT quotients of the symplectic group. The advantage of the above framework is that it applies to the study of closed orbits of an arbitrary Hamiltonian system. Moreover, in the case where the system admits symmetries in the form of ``reflections'', i.e. anti-symplectic involutions, which is the case for many systems of interest, the information provided for orbits which are symmetric is richer, and one may distinguish more symmetric orbits. This is the case for several well-known families in the space mission design industry, such as the Halo orbits, which are ubiquitous in real-life space missions. We will carry out numerical work based on the cell-mapping method, for the Jupiter-Europa and the Saturn-Enceladus systems. These are currently systems of interest, falling in the agenda of space agencies like NASA, as these icy moons are considered candidates for harbouring conditions suitable for extraterrestrial life.

math.SG↗