Dynamic Equations for System of Irregularly Shaped Plane Bodies

Abstract

A cluster of interconnected plane bodies is treated as a discrete system, and each body is considered as an irregularly shaped disk modeled by a system of circular disks bound together by finite bonding forces. The motion of interconnected bodies is governed by the system of differential and algebraic equations in which the differential part is associated with the topological tree and the algebraic one with the constraints imposed by the loops. For an arbitrary topology 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 plane bodies more efficient in terms of both computer time and accuracy. It is achieved by avoiding operations with large sparse matrices (if the equations are generated numerically) and by canceling out some terms in Lagrange's equations analytically.