Effects of the zonal harmonics J2, J3 and J4 on optimal low-thrust trajectories

Effects of the main zonal harmonics on optimal low-thrust limited-power transfers

“…The numerical-analytical procedure described in the previous sections is applied in the analysis of some low-thrust transfers. Preliminary results using the proposed procedure were firstly presented in [34]. Two different classes of transfers are considered: in the first class, variations are imposed on the five orbital elements: semi-major axis, eccentricity, inclination of the orbital plane, longitude of the ascending node and argument of pericenter; in the second class, variations are imposed on only three orbital elements: semimajor axis, eccentricity and inclination of the orbital plane, without terminal constraints on longitude of the ascending node and on argument of pericenter (that is, these orbital elements vary freely).…”

“…So, the reduction in the number of canonical variables simplifies the implementation of the algorithm. If the neighboring extremals algorithm is applied to the original two-point boundary values problem described by the maximum Hamiltonian H * , a system of 156 first-order differential equations (34) p M = 0 must be solved. In turn, the mean two-point boundary value problem involves the solution of a system of 110 first-order differential equations.…”