Mathematical modelling of hanging rope problem subject to rotation

Abstract

The hanging rope problem is considered. The rope is subject to rotation with the rotation axis being parallel to the rope. Using a continuum model and the basic principles of dynamics, the differential equation governing the motion is derived. The dynamic equilibrium case without vibrational motion is assumed in deriving the equation. The equation is cast into a dimensionless form first. It is shown that there are two dimensionless parameters affecting the motion, the dimensionless angular velocity parameter and the dimensionless radius of rotation. The differential equation is solved exactly as well as approximately and the effects of parameters on the motion are discussed in detail. The problem can be discussed in a mechanics or differential equation course at the undergraduate level within the context of applications of differential equations to real-world problems.

KEYWORDS:

• Ordinary differential equations
• hanging rope
• rotation
• dynamic equilibrium

MSC No:

• 34A05
• 34A34
• 74H05

Disclosure statement

No potential conflict of interest was reported by the author.