Use of Equinoctial Orbital Elements as Variables in the Problem of Minimal Time Orbit-to-Orbit Transfer in Strong Gravitational Field under Fixed-Value Thrust

Quasioptimal interorbit transfers of a low-thrust spacecraft in strong central Newtonian gravity field

“…The solution of the problem stated in such a manner gives us the estimation of the maximum allowable value of payload mass M for the case of using variable thrust electric rocket engine, which is characterized by the fixed value of specific mass of power source. The SVs center of mass motion is described by the equations [24] dx j dt = exp( ) jk w k ( j = 1, 5, k = 1, 3),…”

“…The functions jk , 60 and 6k are given in papers [15,24]. The parameters of both the initial and the final orbits are given by the assumptions:…”

“…In the paper [19] the scheme of the averaging was proposed, which made it possible to write down in analytic form the averaged in first approximation equations of motion. The process of averaging is written up in [25] for osculating variables and in [24] for equinoctial ones. In specified papers the integrals of averaged equations are also given that allow to reduce the order of the averaged differential system.…”

“…The components of adjoint vector˜ i in (11) may be calculated with the use of the first integrals specified above and the functions i j are the averaged products i j [24].…”

Optimal low-thrust orbital transfers in a central gravity field

“…The procedure of averaging the equations of optimal motion in equinoctial variables was detailed in [15]. Note that due to the formal inessentiality of the singularity in Eqs.…”