Parameter optimization of atmospheric skip trajectories for use in minimum fuel usage transfer orbits
The problem of developing a generalized impulse as a function of a set of parameters is investigated. The proposed generalized impulse alters an existing orbit by producing, over some period of time, a change in velocity, ΔV, as well as a change in position, Δr. The generalized impulse is described by parameters associated with an instantaneous change in velocity as well as parameters associated with an atmospheric skip trajectory. Closed form solutions are obtained through several changes of independent variable, the use of modified Chapman variables and the consequent analytical integration of the uncoupled equations. The closed form solutions contain between two and six parameters depending on the complexity of the desired skip trajectory. Fuel optimal transfer orbits are obtained using the generalized impulse along with Keplerian arcs and instantaneous changes in velocity. Families of coplanar and noncoplanar transfers for circular orbit to circular orbit are numerically generated. The generated transfer trajectories involve the rendezvous of two vehicles. The orbits are not globally optimal but rather optimal for the specified number and type of velocity impulses specified. The optimal solution to the nonlinear problem is determined via sequential quadratic programming which satisfies the Kuhn-Tucker optimality conditions for constrained minimization. It is found that for transfer between coplanar and noncoplanar orbits, solutions using the generalized impulse compare favorably with solutions obtained by optimal control theory. Numerical solution to complex problems involving transfer from general orbit to general orbit were not obtained.