14 research outputs found
On the motion of a heavy rigid body in an ideal fluid with circulation
Chaplygin's equations describing the planar motion of a rigid body in an
unbounded volume of an ideal fluid involved in a circular flow around the body
are considered. Hamiltonian structures, new integrable cases, and partial
solutions are revealed, and their stability is examined. The problems of
non-integrability of the equations of motion because of a chaotic behavior of
the system are discussed.Comment: 25 pages, 4 figure
The motion of the 2D hydrodynamic Chaplygin sleigh in the presence of circulation
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.Comment: 25 pages, 7 figures. This article uses some introductory material
from arXiv:1109.321