The Hydrodynamic Chaplygin Sleigh

Abstract

We consider the motion of rigid bodies in a potential fluid subject to certain nonholonomic constraints and show that it is described by Euler--Poincaré--Suslov equations. In the 2-dimensional case, when the constraint is realized by a blade attached to the body, the system provides a hydrodynamic generalization of the Chaplygin sleigh, whose dynamics are studied in detail. Namely, the equations of motion are integrated explicitly and the asymptotic behavior of the system is determined. It is shown how the presence of the fluid brings new features to such a behavior.

20 pages, 7 figures

References in corpus (3)

• Motion of a circular cylinder and n point vortices in a perfect fluid
• The Geometry and Dynamics of Interacting Rigid Bodies and Point Vortices
• Some multidimensional integrable cases of nonholonomic rigid body dynamics

Cited by in corpus (6)

• The Chaplygin sleigh with parametric excitation: chaotic dynamics and nonholonomic acceleration
• Fermi-like acceleration and power-law energy growth in nonholonomic systems
• Realizing nonholonomic dynamics as limit of friction forces
• The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation
• Nonholonomic LL systems on central extensions and the hydrodynamic Chaplygin sleigh with circulation
• On the Chaplygin sphere in a magnetic field