A small parameter method in problems of maneuvering space vehicles with aerodynamic efficiency

The motion of a satellite with aerodynamic efficiency along a low near-circular orbit is considered in the paper. The controls of bank angle γ and lift coefficient C y are used as control functions. The introduction of a small parameter ( ϵ = ( ϱ 0 · S · g 0 2G ) ) makes it possible to integrate an adjoint system of equations and to obtain an approximate solution to the complete problem in the class of piecewise-constant control functions. Maximum values for the coordinates of heading angle η and lateral derivation from the plane of a reference orbit ϕ, which are connected with orbit plane angle by the relation cos i = cos ϕ · cos h, are used as criteria of maneuvering capability for a satellite with aerodynamic efficiency. Optimal programs for bank angle and incidence variation are derived and the influence of lift-to-drag ratio on the vehicle maneuvering capabilities has been estimated. It is shown that the process of the optimal motion is a special kind of gravitational skipping similar to the Keplerian motion but with continuous descent.