Numerical solutions for point masses sliding over analytical surfaces: Part 2

作     者：Stefano Tinti Glauco Gallotti 

作者机构：Department of Physics and Astronomy University of Bologna 

出 版 物：《Theoretical & Applied Mechanics Letters》 (力学快报（英文版）)

年 卷 期：2019年第9卷第2期

页      面：96-105页

核心收录：

学科分类：08[工学] 0831[工学-生物医学工程（可授工学、理学、医学学位）] 0830[工学-环境科学与工程（可授工学、理学、农学学位）] 0707[理学-海洋科学] 0815[工学-水利工程] 0805[工学-材料科学与工程（可授工学、理学学位）] 0813[工学-建筑学] 0802[工学-机械工程] 0824[工学-船舶与海洋工程] 0814[工学-土木工程] 0825[工学-航空宇航科学与技术] 0836[工学-生物工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0702[理学-物理学] 

主　　题：Two-point system Rigid-body motion Sliding downslopes 

摘      要：This paper is the second of two companion papers addressing the dynamics of two coupled masses sliding on analytical surfaces and interacting with one another. The motion occurs under the effect of gravity, the reaction force of the surface and basal friction. The interaction force maintains the masses at a fixed distance and lies on the line connecting them. The equations of motion form a system of ordinary differential equations that are solved through a fourth-order Runge–Kutta numerical scheme. In the first paper we considered an approximate method holding when the line joining the masses is almost tangent to the surface at the instant mass positions. In this second paper we provide a general solution. Firstly, we present special cases in which the system has exact solutions. Second, we consider a series of numerical examples where the interest is focused on the trajectories of the masses and on the intensity and changes of the interaction force.