The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation

TL;DR

This paper analyzes the dynamics of a 2D hydrodynamic Chaplygin sleigh with circulation, providing explicit solutions and classifying motion types, relevant for underwater vehicle design.

Contribution

It offers a complete explicit integration of the reduced nonlinear system and classifies all possible motion behaviors.

Findings

Existence of both asymptotic and periodic motions separated by a critical energy level

Complete classification of trajectory types on the plane

Explicit integration of the equations of motion

Abstract

We consider the motion of a planar rigid body in a potential flow with circulation and subject to a certain nonholonomic constraint. This model is related to the design of underwater vehicles. The equations of motion admit a reduction to a 2-dimensional nonlinear system, which is integrated explicitly. We show that the reduced system comprises both asymptotic and periodic dynamics separated by a critical value of the energy, and give a complete classification of types of the motion. Then we describe the whole variety of the trajectories of the body on the plane.