Search results for "Geometric mechanics"

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Geometric Aspects of Mechanics

2010

In many respects, mechanics carries geometrical structures. This could be felt very clearly at various places in the first four chapters. The most important examples are the structures of the space–time continua that support the dynamics of nonrelativistic and relativistic mechanics, respectively. The formulation of Lagrangian mechanics over the space of generalized coordinates and their time derivatives, as well as of Hamilton–Jacobi canonical mechanics over the phase space, reveals strong geometrical features of these manifolds.

PhysicsPoisson bracketsymbols.namesakeGeneralized coordinatesGeometric mechanicsLagrangian mechanicsPhase spaceTangent spacesymbolsRelativistic mechanicsMechanicsAnalytical dynamics
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Singularity formation and separation phenomena in boundary layer theory

2009

In this paper we review some results concerning the behaviour of the incompressible Navier–Stokes solutions in the zero viscosity limit. Most of the emphasis is put on the phenomena occurring in the boundary layer created when the no-slip condition is imposed. Numerical simulations are used to explore the limits of the theory. We also consider the case of 2D vortex layers, i.e. flows with internal layers in the form of a rapid variation, across a curve, of the tangential velocity.

Prandtl's equations Separation Spectral Methods Complex singularities Blow up time Regularizing viscosityBoundary layerClassical mechanicsSingularityDynamical systems theoryGeometric mechanicsDifferential equationComputational mechanicsFluid mechanicsSettore MAT/07 - Fisica MatematicaBoundary element methodMathematicsMathematical physics
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