On the construction and analysis of attainability domains in the Newtonian field (Q1386910)

The motion of a material point in the Newtonian field is considered. Using geometric methods, the problem of constructing attainability domains is studied. Special attention is paid to the cases in which the boundary of attainability domains can be reached by admissible single-impulse control. In these special cases the boundaries of the attainability domains can be described analytically. This theoretical problem may be applied in spacecraft control problems [see e.g. \textit{D. E. Okhotsimskij} and \textit{Yu. G. Sikharulidze}, Foundations of space flight mechanics (in Russian), Moscow, Nauka (1990)]. Several remarks and comments on the attainability problems for finite-dimensional dynamical systems are also presented.