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The motion of the 2D hydrodynamic chaplygin sleigh in the presence of circulation
Fedorov, Yuri; García Naranjo, Luis C.; Vankerschaver, Joris
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
We consider the motion of a planar rigid body in a potential two-dimensional flow with a circulation and subject to a certain nonholonomic constraint. This model can be 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.
Àrees temàtiques de la UPC::Matemàtiques i estadística
Chaplygin sleigh
Fluid-body interaction with circulation
Nonholonomic mechanics
3 entrades relacionades
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::74 Mechanics of deformable solids::74F Coupling of solid mechanics with other effects
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