The Hamiltonian structure of a two-dimensional rigid circular cylinder interacting dynamically with N point vortices
نویسندگان
چکیده
This paper studies the dynamical fluid plus rigid-body system consisting of a two-dimensional rigid cylinder of general cross-sectional shape interacting with N point vortices. We derive the equations of motion for this system and show that, in particular, if the vortex strengths sum to zero and the rigid-body has a circular shape, the equations are Hamiltonian with respect to a Poisson bracket structure that is the sum of the rigid body Lie–Poisson bracket on se(2)*, the dual of the Lie algebra of the Euclidean group on the plane, and the canonical Poisson bracket for the dynamics of N point vortices in an unbounded plane. We then use this Hamiltonian structure to study the linear and nonlinear stability of the moving Föppl equilibrium solutions using the energy-Casimir method. © 2002 American Institute of Physics. @DOI: 10.1063/1.1445183#
منابع مشابه
Discussion on: ''Symmetry Reduction and Control of the Dynamics of a 2-D Rigid Circular Cylinder and a Point Vortex: Vortex Capture and Scattering''
Symmetry reduction and control of the Hamiltonian system of a 2D rigid circular cylinder dynamically interacting with a point vortex external to it is presented. This dynamic model is an idealized example in an inviscid framework of fullycoupled solid-fluid systems interacting in the presence of vorticity and has potential applications to problems in engineering and in nature involving the inte...
متن کامل2 v 1 2 7 D ec 1 99 6 Stabilizing chaotic vortex trajectories : an example of high - dimensional control
A chaos control algorithm is developed to actively stabilize unstable periodic orbits of higher-dimensional systems. The method assumes knowledge of the model equations and a small number of experimentally accessible parameters. General conditions for controllability are discussed. The algorithm is applied to the Hamiltonian problem of point vortices inside a circular cylinder with applications...
متن کاملStabilization of vortices in the wake of a circular cylinder using harmonic forcing.
We explore whether vortex flows in the wake of a fixed circular cylinder can be stabilized using harmonic forcing. We use Föppl's point vortex model augmented with a harmonic point source-sink mechanism which preserves conservation of mass and leaves the system Hamiltonian. We discover a region of Lyapunov-stable vortex motion for an appropriate selection of parameters. We identify four unique ...
متن کاملNumerical Study on Hydrodynamics and Heat Transfer Characteristics Around a Cylinder with Inclined Splitter Plates
In the current paper, the effect of length and angle of a splitter plate on hydro-thermal field in a range of Reynolds number from 40 to 1000 are numerically studied by solving the two-dimensional Navier-Stokes equations. For discretization of governing equations, PISO algorithm was imposed to segregate the pressure-velocity coupled equations, and second-order upwind discretization scheme was a...
متن کاملDynamic Response of Submerged Vertical Cylinder with Lumped Mass under Seismic Excitation
An analytical approach is presented to assess the response of offshore structures under seismic excitation. This paper evaluates the impacts of different fluid field models and the mass of equipment at the top of offshore structure which is simulated as lumped mass on the responses of offshore structures. To do this, two and three dimensional fluid field models are developed. In three dimension...
متن کامل