Abstract Quasi-periodic invariant tori are of great interest in astrodynamics because of their capability to further expand the design space of satellite missions. However, there is no general consent on what is the best methodology for computing these dynamical structures. This paper compares the performance of four different approaches available in the literature. The first two methods compute invariant tori of flows by solving a system of partial differential equations via either central differences or Fourier techniques. In contrast, the other two strategies calculate invariant curves of maps via shooting algorithms: one using surfaces of section, and one using a stroboscopic map. All of the numerical procedures are tested in the co-rotating frame of the Earth as well as in the planar circular restricted three-body problem. The results of our numerical simulations show which of the reviewed procedures should be preferred for future studies of astrodynamics systems.
Fully Numerical Methods for Continuing Families of Quasi-Periodic Invariant Tori in Astrodynamics
The Journal of the Astronautical Sciences ; 65 , 2 ; 157-182
2018-01-16
26 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
Dynamical systems theory , Quasi-periodic invariant tori , Continuation , Partial differential equations , Boundary value problems Engineering , Aerospace Technology and Astronautics , Mathematical Applications in the Physical Sciences , Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics)
Fully Numerical Methods for Continuing Families of Quasi-Periodic Invariant Tori in Astrodynamics
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