Decomposition of the phase portrait of a dynamic system controlled by fiber bundle

A geometrical approach is proposed to development of a phase portrait of a dynamic system with control, DSC in the state space. The fiber boundle tools yield the Ilamiltonian of the reduced CDS on the bundle face. Earlier results on two-dimensional phase portraits are applied to such reduced DSC and are enlightening in analyse is of various controllability and attainability properties of linearly controlled DSCs in a three-dimensional space.