A theory of flying/swimming saucers. Exact solutions for rectilinear locomotion

TL;DR

This paper presents exact analytical solutions for rectilinear self-propulsion of a robot or underwater vehicle in an inviscid fluid, demonstrating two locomotion modes and their efficiency, with implications for testing models and educational use.

Contribution

It introduces two classes of exact solutions for rectilinear locomotion in inviscid fluids, highlighting the efficiency of tumbling motion and the applicability of actuator control for directed movement.

Findings

Tumbling locomotion is more efficient than zigzag.

Actuator control enables arbitrary direction and speed.

Solutions are simple enough for educational purposes.

Abstract

We study self-propulsion (or locomotion) of a robot (or an underwater vehicle) in an inviscid incompressible fluid. The robot's body is rigid, while its locomotion ability is due to an internal actuator, which can perform controlled translational and rotational oscillations. Our attention is focused on two classes of the plane analytic exact solutions, describing rectilinear locomotion. Solutions of the first class describe the \emph{tumbling locomotion}, while the second class corresponds to the \emph{zigzag locomotion} without tumbling. We show, that tumbling locomotion is more efficient. Both classes of solutions show, that the use of actuator allows to choose any desired direction and any speed of locomotion. As a special case, we consider the self-propulsion caused by small-amplitude and high-frequency actuator oscillations. The exact and elementary character of our solutions makes the results potentially useful as the tests to verify physical and engineering models, as well as numerical and asymptotic results. In contrary to many recent publications in this area, the material is accessible to UG students in Engineering, Physics, and Applied Mathematics.