Generation of Motion Equations for a Tree-Like System of Granular Bodies

An arbitrary system of 3D-bodies made out of rigid spheres and arranged topologically in a tree is considered. For such a system explicit expressions for the equations of motion are derived based on the Lagrangian approach. The equations are given in terms of the path matrix characterizing the topological tree. The analytical method of generation of equations of motion makes the computer simulation of the nonsteady motion of the discrete system of bodies more efficient in term of both computer time and accuracy. It is achieved by avoiding operations with large sparse matrices (if the equations were generated numerically) and by cancelling out some terms in Lagrange’s equations analytically.