Kinematics of a Holonomic Constraint Rod & Cube System

Abstract

A loose rod of mass m1 and length l leans against one of the faces of a cube of mass m 2 and side length a . The assembly is placed on a horizontal table with one end of the rod touching the table and its other end leaning against the edge of the cube. We set the rod and the center of mass of the cube on the same vertical plane, and then we release the assembly from the rest. For frictionless contacts, we calculate the separation runtime of the rod from the cube as a function of m 2 / m 1 and a / l . This entails forming the equation describing the motion of the system. The equation of motion is analytically unsolvable nonlinear differential equation. Applying a Computer Algebra System, specifically Mathematica [1] [2], we solve the equation numerically. Utilizing the solution, in addition to evaluating the separation runtime, we quantify a list of dynamic quantities, such as the time-dependent interface forces, and, geometric quantities, such as the trajectory of the loose end of the rod. A robust Mathematica code addresses the “what if” scenarios.