Control of body motion in an ideal fluid using the internal mass and the rotor in the presence of circulation around the body

TL;DR

This paper investigates controlling the motion of a 2D ideal fluid body with internal mechanisms, showing how internal mass and rotor adjustments enable movement towards a target point despite circulation effects.

Contribution

It introduces control strategies for body motion in an ideal fluid with circulation, highlighting limitations and possibilities for stabilization and movement control.

Findings

Internal mass and rotor control can direct the body to a target point.

Circulation prevents complete stabilization at arbitrary points.

Simple control schemes can achieve near-target positioning.

Abstract

In this paper we study the controlled motion of an arbitrary two-dimensional body in an ideal fluid with a moving internal mass and an internal rotor in the presence of constant circulation around the body. We show that by changing the position of the internal mass and by rotating the rotor, the body can be made to move to a given point, and discuss the influence of nonzero circulation on the motion control. We have found that in the presence of circulation around the body the system cannot be completely stabilized at an arbitrary point of space, but fairly simple controls can be constructed to ensure that the body moves near the given point.