基于外积求解颗粒平衡问题

Solving Particle Equilibrium Problem Based on Wedge Product

提出一种简洁有效的基于外积的方法,对无摩擦的二维圆盘、二维凸颗粒以及三维球体的力学平衡方程进行求解和分析。理论结果表明,圆盘与球体上输出力的大小与输入力的大小成正比,因此引入了力传递的概念,并且导出力传递系数与接触结构的关系。对于凸颗粒,导出了输出力大小与输入力以及力矩的关系式。在已知圆盘上的平均正压力时,导出了各个接触力大小的公式并给出其几何意义。文中提出的方法以及计算的结果,对于求解其他物理问题中的向量方程有意义,对于进一步研究力学网络上的平衡方程有重要价值。

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.