  This paper aims to present a general idea for description of spatially finite
physical objects with a consistent nontrivial translational-rotational
dynamical structure and evolution as a whole, making use of the mathematical
concepts and structures connected with the Frobenius
integrability/nonintegrability theorems given in terms of distributions on
manifolds with corresponding curvature defined by the Nijenhuis operator. The
idea is based on consideration of {\it nonintegrable} subdistributions of some
appropriate completely integrable distribution (differential system) on a
manifold and then to make use of the corresponding curvatures as generators of
measures of interaction, i.e. of energy-momentum exchange among the physical
subsystems mathematically represented by the nonintegrable subdistributions.
The concept of photon-like object is introduced and description of such objects
in these terms is given.
