منابع مشابه
Hamiltonian Fluid Mechanics
where x = φ(X, T ) is the position of the material point X at time T . We will refer to X as a material, or Lagrangian point, and x as a spatial or Eulerian point. If Ω ⊂ B is a material region, we denote by ΩT = φ (Ω, T ) the spatial region occupied by the material points in Ω at time T . We assume that the deformation φ is smooth, with a smooth inverse X = Φ(x, t). Here, we write T = t for th...
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We suggest the Hamiltonian approach for fluid mechanics based on the dynamics, formulated in terms of Lagrangian variables. The construction of the canonical variables of the fluid sheds a light on the origin of Clebsh variabes, introduced in the previous century. The develoted formalism permitts to relate the circulation conservation (Tompson theorem) with the invariance of the theory with res...
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Comment on " Berry phase correction to electron density in solids " by Xiao et al. Abstract The main result of Xiao et al. In a recent paper on the semiclassical dynamics of a Bloch electron, Xiao, Shi and Niu [1] claim that, due to a Berry curvature term, Liouville's theorem on the conservation of the phase-space volume element would be violated, a fact which would have been overlooked so far....
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Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in fourdimensional space–time represents the relativistic invariance by the equation for four-velocity ulu + c = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in fou...
متن کاملDiscrete variational Hamiltonian mechanics
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ژورنال
عنوان ژورنال: Annual Review of Fluid Mechanics
سال: 1988
ISSN: 0066-4189,1545-4479
DOI: 10.1146/annurev.fl.20.010188.001301