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

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.

25 pages, 7 figures. This article uses some introductory material from arXiv:1109.3210

References in corpus (5)

• Motion of a circular cylinder and n point vortices in a perfect fluid
• The Geometry and Dynamics of Interacting Rigid Bodies and Point Vortices
• The Dynamics of a Rigid Body in Potential Flow with Circulation
• Geometry of Invariant Tori of Certain Integrable Systems with Symmetry and an Application to a Nonholonomic System
• Nonholonomic LL systems on central extensions and the hydrodynamic Chaplygin sleigh with circulation

Cited by in corpus (5)

• The dynamics of an articulated $n$-trailer vehicle
• Fermi-like acceleration and power-law energy growth in nonholonomic systems
• Nonholonomic LL systems on central extensions and the hydrodynamic Chaplygin sleigh with circulation
• Persistence of stationary motion under explicit symmetry breaking perturbation
• On the Chaplygin sphere in a magnetic field