Eventos Anais de eventos
COBEM 2019
25th International Congress of Mechanical Engineering
Effects of the zonal harmonics J2, J3 and J4 on optimal low-thrust trajectories
Submission Author:
Sandro da Silva Fernandes , SP
Co-Authors:
Sandro da Silva Fernandes, Francisco das Chagas Carvalho
Presenter: Francisco das Chagas Carvalho
doi://10.26678/ABCM.COBEM2019.COB2019-0356
Abstract
In this work, a numerical-analytical procedure based on infinitesimal canonical transformation is developed for computing optimal time-fixed low-thrust limited power transfers between arbitrary orbits in Earth´s gravitational field which includes the effects of the zonal harmonics J2, J3 and J4. The proposed procedure involves the development of a two-stage algorithm: in the first step, a neighboring extremals algorithm is applied to solve the two-point boundary-value problem governed by an average canonical system describing the secular behavior of the optimal trajectories; in the second step, a Newton-Raphson algorithm is applied to adjust the initial values of the adjoint variables when the first order periodic terms are included. The maximum Hamiltonian governing the average canonical system is computed by applying the concept of ‘mean Hamiltonian’, and, the first order periodic terms due the second zonal harmonic J2 and the optimal thrust acceleration are recovered by means of Hori method. Some numerical results show the effects on the optimal trajectories due the zonal harmonics considered in this study.
Keywords
Low-thrust transfers, Optimal Space Trajectories, Zonal harmonics
