On the astrodynamics applications of Weierstrass elliptic and related functions

2016/01/19 by Dario Izzo, Francesco Biscani, Izzo, Dario +1
Engineering · Mathematics · Physics and Astronomy · #Astro and Planetary Science #Cosmology and Gravitation Theories #Earth and Planetary Astrophysics (astro-ph.EP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Spacecraft Dynamics and Control #astro-ph.EP #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.1601.04963

Presented at the AAS/AIAA Space Flight Mechanics Meeting, Napa, CA in February 14, 2016

openalex publication_date 2016/01/19 · arxiv created 2016/01/20 · arxiv updated 2016/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Weierstrass elliptic and related functions have been recently shown to enable analytical explicit solutions to classical problems in astrodynamics. These include the constant radial acceleration problem, the Stark problem and the two-fixed center (or Euler's) problem. In this paper we review the basic technique that allows for these results and we discuss the limits and merits of the approach. Applications to interplanetary trajectory design are then discussed including low-thrust planetary fly-bys and the motion of an artificial satellite under the influence of an oblate primary including J₂ and J₃ harmonics.

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