Abstract
A model for the motion of a granular medium is proposed, which is based on the elastic interaction of particles each of which is a perfectly rigid body (a disk in the planar case and a sphere in the spatial case) of mass m and radius r, surrounded by a sufficiently thin elastic shell. An algorithm for solving the formulated problem is proposed. At each step, the forces and moments of forces arising from the interaction of a particle with neighboring particles are calculated. The Cauchy problem for the resulting system of differential equations was numerically solved. Based on the mathematical model, a set of programs was developed that simulates the behavior of granular media in moving containers.
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