A kinetics equation for a singular beam of particles in an external forces field

A geometrical formalism is presented for dynamics of ensembles of particles, which are localized on a manifold surface of a classical phase space and are named “singular beams” in this paper. An equation of the singular beam dynamics is obtained in the simplest case of an external forces field, as well as an integral conservation law for the beam particles in an arbitrary volume of a phase space is derived. A coordinate representation of the obtained equation is considered, and a number of examples is discussed in the text.