Validated semi-analytical transition matrices for linearized relative spacecraft dynamics via Chebyshev series appproximations

Paulo Ricardo Arantes Gilz (1) , Florent Bréhard (1, 2, 3) , Clément Gazzino (1)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 ARIC - Arithmetic and Computing
3 PLUME - Preuves et Langages

We provide an efficient generic algorithm to compute validated approximations of transition matrices of linear time-variant systems using Chebyshev expansions, and apply it to two different examples of relative motion of satellites (spacecraft rendezvous with Tschauner-Hempel equations and geostationary station keeping with J2 perturbation in the linearized Orange model).

Mots clés: Chebyshev expansions; relative motion; control theory; linear differential equations; space flight dynamics; rigorous numerics

Domaines: Informatique [cs]; Sciences de l'ingénieur [physics]; Planète et Univers [physics]

Paulo Ricardo Arantes Gilz, Florent Bréhard, Clément Gazzino. Validated semi-analytical transition matrices for linearized relative spacecraft dynamics via Chebyshev series appproximations. 2018 Space Flight Mechanics Meeting, AIAA Science and Technology Forum and Exposition 2018, Jan 2018, Kissimmee, United States. 24p. ⟨hal-01540170v1⟩