My primary research areas are celestial mechanics, dynamical systems, and astrodynamics. In particular, I am interested in connections between these fields. On the one hand, space mission design saw great advancements in the early 2000s by incorporating techniques of dynamical systems theory, and there are more improvements to be made. On the other hand, there are many interesting mathematics problems arising from cislunar astrodynamics and solar system dynamics, including some of the most foundational questions in the field of dynamical systems. Thus, my work connects the two ends of this spectrum from Applied Mathematics (celestial mechanics & dynamical systems) to Aerospace Engineering (astrodynamics). My PhD thesis focuses on unifying semi-analytical and numerical methods for applications to astrodynamics. A list of research interests can be found at the bottom of this page.
Publications and Preprints
"Local Orbital Elements with Halo Orbits," with E. Dennis and D. Scheeres. 2025 AAS/AIAA Astrodynamics Specialist Conference.
"The Structure of Periodic Orbit Families in the Hill Restricted 4-Body Problem," with G. Brown, D. Henry, and D. Scheeres. SIAM Journal on Applied Dynamical Systems (2025).
"Unifying Semi-analytical and Numerical Methods for Astrodynamics Applications." Dissertation (2024).
"Dynamics of the 9:2 Near Rectilinear Halo Orbit in the Sun-Earth-Moon System: Staging, Phasing, and Transitioning," with G. Brown, B. McCarthy, D. Henry, D. Scheeres, and D. Davis. International Astronautical Congress.
"Behavior of the Lunar Gateway's Planned Orbit in the Sun-Earth-Moon System," with G. Brown, D. Henry, and D. Scheeres. 2024 AAS/AIAA Astrodynamics Specialist Conference.
"Local Orbital Element Toolkit in Cislunar Space," with D. Scheeres. 2024 AAS/AIAA Astrodynamics Specialist Conference.
"Gauss Equations for Local Orbital Elements in Cislunar Space," with D. Scheeres. Journal of Guidance, Control, and Dynamics (2024).
"Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem ," with G. Brown, À. Jorba, and D. Scheeres. Celestial Mechanics & Dynamical Astronomy (2024).
"The Vicinity of Earth-Moon L1 and L2 in the Hill Restricted 4-Body Problem," with J. Rosales and D. Scheeres. Physica D: Nonlinear Phenomena (2023).
"Local Orbital Elements for the Circular Restricted Three-Body Problem," with D. Scheeres. Journal of Guidance, Control, and Dynamics (2023).
"O2- and CO-rich Atmospheres for Potentially Habitable Environments on TRAPPIST-1 Planets," with R. Hu and E. Wolf. The Astrophysical Journal (2020).
In Preparation:
"Local Cislunar Orbital Elements with Halo Orbits," with E. Dennis, À. Jorba, and D. Scheeres.
"Computer-Assisted Proofs for the Persistence of Resonant Periodic Orbits in the Sun-Earth-Moon-Particle System," with G. Brown, J. Mireles-James, and D. Scheeres.
"Ejection-Collision Orbits in the Spatial Circular Restricted 3-Body Problem," with J. Gimeno and J. Mireles-James.
"Local Orbital Elements Around a Periodic Orbit in the Circular Restricted 3-Body Problem," with J. Gimeno and À. Jorba.
Software
Research Interests
Celestial Mechanics
Problems in realistic solar system models
Restricted 3- and 4-body problems
Normal forms
Regularization of singularity
Long-time stability estimates
Dynamical Systems
Hamiltonian systems
Perturbation theory: KAM, Melnikov
Computation of invariant manifolds: parameterization method, center manifold reduction
Continuation of periodic, quasi-periodic, heteroclinic solutions
Computer-assisted Proofs in Dynamics
Astrodynamics
Cislunar astrodynamics
Transfer design
Space situational awareness
Applications to Lunar Gateway
Incorporating computational methods of applied mathematics to mission design practice