I am an NSF Mathematical Sciences Postdoctoral Research Fellow in the Mission Design and Navigation Section (392K) of the NASA Jet Propulsion Laboratory, California Institute of Technology. I completed my Ph.D. in 2022 from the School of Mathematics at Georgia Tech, advised by Prof. Rafael de la Llave and supported by a NASA NSTRF fellowship. I also spent time during my Ph.D. as an NSTRF visiting technologist at JPL working with mentor Dr. Rodney Anderson. Prior to that, from 2014-2017 I was a co-op student in the Radio Science Systems Group (332K) at JPL.
- Ph.D. Mathematics, Georgia Institute of Technology, 2022
- M.S. Aerospace Engineering, Georgia Institute of Technology, 2021
- B.S. Mathematics, Georgia Institute of Technology, 2015
- B.S. Aerospace Engineering, Georgia Institute of Technology, 2015
At a broad level, my interests lie in the application of tools and results from mathematical dynamical systems theory, both analytical and computational, to various problems in celestial mechanics and applied astrodynamics for space mission design. In brief, there are geometric structures, such as periodic orbits, invariant tori, and stable and unstable manifolds, which govern many of the important dynamical properties of multi-body celestial systems. I am interested in developing fast and accurate methods for computing these objects as well as for investigating the dynamics induced by them. I am also working on applications of these methods to current and relevant problems in astrodynamics, with a current focus on tour design in multi-moon systems using mean motion resonances.
- NSF Mathematical Sciences Postdoctoral Research Fellow, Mission Design and Navigation, JPL (2022-present)
- NSTRF Student Visiting Technologist, Mission Design and Navigation, JPL (2018-2022)
- Graduate Student Researcher in Mathematics, Georgia Tech (2015-2022)
- Engineering Co-op Student, Radio Science Systems, JPL (2014-2017)
- Top Graduate Student Award of the Georgia Tech School of Mathematics
- National Science Foundation Mathematical Sciences Postdoctoral Research Fellowship. Grant DMS-2202994, 2022
- NASA Space Technology Research Fellowship (NSTRF18). Grant 80NSSC18K1143, 2018
- B. Kumar, R.L. Anderson, and R. de la Llave (2023). “Rapid GPU-Assisted Search & Parameterization-Based Refinement and Continuation of Connections between Tori in Periodically Perturbed Planar Circular Restricted 3-Body Problems,” submitted to SIAM Journal on Applied Dynamical Systems. arXiv:2109.14814.
- B. Kumar, R.L. Anderson, and R. de la Llave (2023). “4th Body-Induced Secondary Resonance Overlapping Inside Unstable Resonant Orbit Families: a Jupiter-Ganymede 4:3 + Europa Case Study,” 2023 AAS/AIAA Astrodynamics Specialist Conference, Big Sky, USA, August 2023. Paper AAS 23-397. arXiv:2309.06073.
- B. Kumar, R.L. Anderson, and R. de la Llave (2023). “Transfers between Jupiter-Ganymede and Jupiter-Europa Resonant Tori In a Concentric Circular Restricted 4-Body Model,” Acta Astronautica 211(2023): 76–87. doi:10.1016/j.actaastro.2023.05.040.
- B. Kumar, R.L. Anderson, and R. de la Llave (2022). “Rapid and Accurate Methods for Computing Whiskered Tori and Their Manifolds in Periodically Perturbed Planar Circular Restricted 3-Body Problems,” Celest Mech Dyn Astron 134:3. doi:10.1007/s10569-021-10057-1.
- B. Kumar, R.L. Anderson, R. de la Llave, and B. Gunter (2021). “Computation and Analysis of Jupiter-Europa and Jupiter-Ganymede Resonant Orbits in the Planar Concentric Circular Restricted 4-Body Problem,” 2021 AAS/AIAA Astrodynamics Specialist Conference, Virtual, August 2021. Paper AAS 21-651. arXiv:2109.14815.
- B. Kumar, R.L. Anderson, and R. de la Llave (2021). “High-Order Resonant Orbit Manifold Expansions For Mission Design In the Planar Circular Restricted 3-Body Problem,” Commun Nonlinear Sci Numer Simulat 97(2021): 105691. doi:10.1016/j.cnsns.2021.105691.
