Trajectory of a Circular System

Abstract

Consider an infinitely long massless rod with a movable mass m attached, assuming a frictionless interaction between the rod and the mass. The rod undergoes rotational motion with a constant angular velocity α about a fixed pivot point O, causing the mass to move outward along its length. The objective is to determine the trajectory of the mass, specifically deriving the functional relationship between the radial coordinate r and the angular coordinate θ.

Keywords: Ordinary Differential Equation, Dynamical System