The model of ball-shaped partiсle with nonuniform active surface in the rarefied gas is constructed. The features of appropriate dynamical system are established. The lemma on the properties of high-dimension ODE is proved. This lemma is an important step, providing an opportunity to find solution corresponding to various types of asymptotic of the partiсle motion.

solid paticle dynamics, rarefied gas, nonuniform active surface, ODE, invariant sets, asymptotic properties, asymptotically stable trajectory

Mathematical modelling in actual problems of science and technics