OPTIMAL LOW-THRUST TRANSFERS BETWEEN ELLIPTIC COAXIAL NONCOPLANAR ORBITS

Sandro da Silva Fernandes¹; Francisco das Chagas Carvalho¹

¹ Instituto Tecnológico de Aeronáutica

doi:10.20906/CPS/COB-2015-0477

Resumo

The analysis presented in this work has been motivated by the renewed interest in the use of low-thrust propulsion systems in space missions in the last thirty years. Important space missions have made use of low-thrust propulsion systems: NASA-JPL Deep Space 1 and ESA-SMART1. Low-thrust electric propulsion systems are characterized by high specific impulse and low-thrust capability (the ratio between the maximum thrust acceleration and the gravity acceleration on the ground is small, between 104 and 102) and have their greatest benefits for high-energy planetary missions. Several researchers have obtained numerical and analytical solutions for several maneuvers involving specific initial and final orbits and specific thrust profiles. In the analytical studies, averaging techniques are applied and solutions of the averaged equations are obtained such that only secular behavior of the optimal solutions is discussed. Few works discuss the inclusion of periodic terms which are, in general, considered only for transfers between close orbits or for transfers between arbitrary elliptic coplanar orbits. So, the main goal of this work is to obtain an approximated analytical solution, which includes short periodic terms, for the problem of optimal time-fixed low-thrust limited-power transfers (no rendez-vous) between elliptic coaxial noncoplanar orbits in a Newtonian central gravity field. The optimization problem is formulated as a Mayer problem of optimal control theory with semi-major axis, eccentricity and inclination or longitude of the ascending node - as state variables. After applying the set of necessary conditions provided by Pontryagin Maximum Principle and determining the maximum Hamiltonian which describes the extremals trajectories, the short periodic terms are eliminated through an infinitesimal canonical transformation built through Hori method - a perturbation canonical method based on Lie series. The new maximum Hamiltonian resulting from the infinitesimal canonical transformation descr

Palavras-chave: Low thrust transfers; Optimization of space trajectories; Coaxial noncoplanar orbits