Some general properties of collision integral. Oriented particles

The matrix elements (ME) of the Boltzmann collision integral (CI) are studied. Two types of the particles under collisions are considered. For the oriented particles, a minimum set of the linear MEs using the relationships between MEs is found through which any MEs can be expressed. The universal coefficients of these expressions are built, which are not affected by an interaction cross section. In the case of the standard non-oriented particles, the simple kernels of the non-linear collision operator are built with MEs giving an opportunity to reject the limitations involved via the Grad criterion and to make possible the boundary problems solution.