Optimal output of satellite in geostationary orbit, taking into account costs of inefficient fuel consumption when the engine is switched on and off
Space technics and technology
AbstractWe consider the problem of transition artificial Earth satellite with an initial circular orbit to geosynchronous orbit with minimum fuel consumption. Solution in the classical setting (in the class of continuous systems) leads to an infinite sequence of impulse inclusions (at extremely the little time) of the engine with a maximum thrust of around pericenters on osculating orbits. The total fuel consumption becomes less at this mode, but the overall stabilization time increases unlimitedly. Therefore, we have considered the problem in view of inefficient fuel consumption (in the class of logic-dynamical systems). Approximate solution is based on necessary optimality conditions of logical-dynamic systems. A comparison of the conditions necessary to apply the maximum principle. The results of calculations in a classical setting, and for logic-dynamical systems, as well as their practic applicability, are discussed.
Keywords:geostationary orbit, logical-dynamical systems, the necessary conditionsfor optimality.