Applied Physics and Mathematics Annotation << Back Determination of potential component of the vector field of control system by constructing a homotopy operator S.N. Chukanov A method for decomposing a vector field of a dynamical system based on the construction of homotopy operator is proposed in this paper. The vector field is decomposed on the exact component corresponding to the gradient vector field, and anti-exact component. In the case of a linear dynamic system the decomposition leads to components, corresponding representations of the symmetric and skew-symmetric matrices. The method can be used to construct systems of dynamic systems. The method can be used to construct systems of dynamic systems for the study of system stability. The inverse problem of the dynamics of the controlled system of finding the vector potential forces for the formation of system movement on the required trajectory is considered. The use of the foregoing decomposition method for dynamical systems described by first order differential equations, allows to form the Lagrangian that Euler-Lagrange equations will correspond the original differential equations. Keywords: decomposition of the vector field, stability of control system, Lyapunov function, operator of homotopy, inverse problem of dynamics. Contacts: E-mail: ch_sn@mail.ru Pp. 40-46.