АНАЛИТИЧЕСКИЕ РЕШЕНИЯ ДЛЯ УЧАСТКОВ МАЛОЙ ТЯГИ В ЦЕНТРАЛЬНОМ НЬЮТОНОВСКОМ ПОЛЕ

the aim of the research was to identify the existing problem in optimizing the movement of a point of variable mass (the center of mass of the spacecraft - SC) in a gravitational field. It includes the selection, forecasting, optimization and calculation of trajectories of managed objects. The following are some of their recent results. The variational problem in the formulation of Louden is to determine the controls (magnitude and direction of the reactive force) and the optimal trajectories of a point moving with a limited second mass flow rate m.The end result of the variational problem, in the definition of controls, is the magnitude and direction of the traction force that transfers a point from a given position to a certain final one, and also minimizes the mass consumption. In this work, the analytical solutions of the variational problem differ from the solutions: Lowden spirals differ in the law of mass change (lowthrust),and, consequently, in the values of the parameters and characteristics of the engine. The resulting trajectories can find application in problems ofescape and maneuvers of transition from orbit to orbi