Solving Particle Equilibrium Problem Based on Wedge Product
A simple and effective method based on exterior product is proposed to solve and analyze the mechanical equilibrium equations for frictionless particles with different shapes such as two-dimensional disk,two-dimensional convex particle and three-dimensional sphere.The theoretical results show that the output force on a disk or a sphere is proportional to the input force.Therefore,the concept of force transmission is introduced,and the relationship between the coefficient of force transmission and the contact structure is derived.For case of convex particle,the relationship between the output force and the input force and torque is derived.When the average normal pressure on a disk is known,the formulas of the contact forces are derived and their geometric significances are given.The method and results presented in this paper are also significant for solving vector equations in other physical problems and for further studying the equilibrium equations on mechanical networks.
granular mattermechanical equilibriumtensor algebrawedge productcoefficient of force trans-mission
万方数据
维普
