Applied Physics and Mathematics Annotation << Back THE DETERMINATION OF INVARIANTS OF SYSTEM TRAJECTORIES DESCRIBED BY DIFFERENTIAL AND DIFFERENCE EQUATIONS S.N. CHUKANOV The method for determining system trajectory invariants based on an artificial closure of a trajectory is considered. Trajectory parameters are presented in the form of the product integrals. Formed invariants do not depend on the initial conditions of the equations. An example is given of finding the geometric phase of the rotational motion of the axes of a coordinate system of a rigid body. Keywords: invariants of trajectory, product integral, rotation motion of axes, rigid body. DOI: 10.25791/pfim.01.2019.499 Contacts: E-mail: ch_sn@mail.ru Pp. 43-48.