Chapter 3.5, Problem 1E

Interpretation Introduction

Interpretation:

To explain in physical terms why the bead cannot have an equilibrium position with $\varphi >\frac{\text{π}}{\text{2}}$

Concept Introduction:

The supercritical pitchforkis also called forward bifurcation. It closely shows a continuous or second-order phase transition.

In statistical mechanics, the subcritical bifurcation is sometimes called inverted or backward bifurcation, and it is related to discontinuous or first order phase transition.

A bead of mass m slides along a wire hoop of radius r. The hoop is constrained to move at a constant angular velocity $\omega$ about its vertical axis.