Thrust limited coplanar aeroassisted orbital transfer

Two fuel-minimal aeroassisted orbital transfers are examined, Transfers from geosynchronous orbit to a low Earth orbit are considered, Instead of assuming an impulsive thrust on initial and final orbit, limited thrust on a nonvanishing interval on each orbit is introduced. In the atmospheric part, the transfer vehicle is controlled via the lift coefficient. The influence of Earth's rotation is considered also. Whereas in the atmospheric part an Earth-fixed frame of reference is used, the nonatmospheric parts are considered in an inertial frame of reference. This leads to an optimal control problem with well-defined jumps in the state and adjoint variables at the junction points between atmospheric and nonatmospheric arcs, The necessary conditions, including adjoint differential equations, boundary and interior point conditions, and control conditions, are derived to set up a boundary; value problem. Solutions for a high and a low maximum magnitude of thrust with Earth's rotation, first neglected and later included, are presented.