On investigation of systems with first integrals

The paper proposes some approaches which allow to find first integrals for the systems of ordinary differential equations, to reduce them to the most trivial form and use them for constructing the phase space. These results have already given the possibility to obtain new information on stationary sets of first integrals in solid body dynamics and in dynamics of a set of solid bodies. These applied problems are interesting, in particular, for the fact that rather complex attracting sets (so called strange attractors) are possible in such systems [1]. Some examples of application of the approach proposed for analysis of concrete mechanical systems are considered.