可変推力による楕円軌道間飛しょう体移行の最適制御

抄録

This paper deals with the minimum-fuel transfer between neighboring elliptic orbits for a low-thrust power-limited propulsion system. Since an initial and a target orbit are located close to each other, the inclination between orbit planes is small and the radial separation between orbits is also small relative to the semilatus rectum of either orbit. This condition may allow the assumption that the motion in the transfer does not deviate significantly from the terminal orbits and that linearization of the gravitational terms in the equation of motion is permissible. In the case of circular terminal orbits, the equation of motion of the vehicle becomes a linear differential equation with constant coefficients; and the exact solution is obtained analytically. The orbital velocity of a vehicle revolving along an elliptic orbit varies periodically in time. This variation produces terms with periodic coefficients in the equation of motion; furthermore it results in the variation of fuel consumption with respect to position of the point of departure.
When the eccentricities of the orbits are small, the time-varying terms in the equation of motion are also small. The small parameter method is applied for obtaining an approximate solution of the differential equation with periodic coefficients. The optimal thrust program is investigated by using Pontryagin's maximum principle. The motion of the vehicle and the fuel consumption under the action of the optimal thrust are also studied. The result obtained clarifies dependence of the fuel consumption on the transfer time and on the position of departure from the initial orbit.