Abstract

FERNANDES, Sandro da Silva; CARVALHO, Francisco das Chagas  and  ROMAO, João Victor Bateli. A numerical-analytical approach based on canonical transformations for computing optimal low-thrust transfers. Rev. mex. astron. astrofis [online]. 2018, vol.54, n.1. ISSN 0185-1101.

A numerical-analytical procedure based on infinitesimal canonical transformations is developed for computing optimal time-fixed low-thrust limited power transfers (no rendezvous) between coplanar orbits with small eccentricities in an inverse-square force field. The optimization problem is formulated as a Mayer problem with a set of non-singular orbital elements as state variables. Second order terms in eccentricity are considered in the development of in the maximum Hamiltonian describing the optimal trajectories. The two-point boundary value problem of going from an initial orbit to a final orbit is solved by means of a two-stage Newton-Raphson algorithm which uses an infinitesimal canonical transformation. Numerical results are presented for some transfers between circular orbits with moderate radius ratio, including a preliminary analysis of Earth-Mars and Earth-Venus missions.

Keywords : celestial mechanics; methods: analytical; methods: numerical.

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