ИНТЕГРИРУЕМЫЕ СИСТЕМЫ НА КАСАТЕЛЬНОМ РАССЛОЕНИИ К МНОГОМЕРНОЙ СФЕРЕ
The systems which have ﬁnite-dimensional spheres as the space of positions, are arising in many problems of multi-dimensional dynamics. Accordingly, tan- gent bundles of those spheres become phase spaces of such systems. In the article activity of inductive transition in the system on tangent bundle of low-dimen- sional sphere under increase of its dimension and absence of force ﬁeld is ana- lyzed. At that, nonconservative ﬁelds of forces are presented with the presence of which the systems possess the complete choice of ﬁrst integrals expressing in terms of ﬁnite combination of elementary functions and are, in general, the transcendental functions of its variables.