On the dynamics of rotating rigid tube and its interaction with air

Abstract

Rotating an axially symmetric rigid body on a horizontal plane is rather a common and simple experience, but this experience has attracted a great deal of interests due to it exhibiting novel features and containing fairly complicated mechanics. This paper is concerned with the three-dimensional rotational motion of a rigid tube on a plane. We present the governing dynamical equations of this motion and give a numerical treatment, based on which we discuss the nutation of tube and simulate the trajectory of tube end. We also discuss how fast the angular velocity should be in order to initiate an uninterrupted, steady rotational motion. Then the air lift related to such a three-dimensional rotation of tube is modeled by using Kutta-Joukowski law. By employing this model, we show that the air lift indeed “lift” the tube head during rotating.