منابع مشابه
Lagrangian and Hamiltonian Methods in Geophysical Fluid Dynamics
This note is an introduction to the variational formulation of fluid dynamics and the geometrical structures thus made apparent. A central theme is the role of continuous symmetries and the associated conservation laws. These are used to reduce more complex to simpler ones, and to study the stability of such systems. Many of the illustrations are taken from models arising from geophysical fluid...
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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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Hamiltonian systems are a class of dynamical systems which can be characterised by preservation of a symplectic form. This allows to write down the equations of motion in terms of a single function, the Hamiltonian function. They were conceived in the 19th century to study physical systems varying from optics to frictionless mechanics in a unified way. This description turned out to be particul...
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Gliders are new marine vehicles which have research and military uses and they move by sequent diving and climbing. Suitable design of its main body and wings are important for the most advance velocity. hydrodynamic design variables are main body form, wings (cross section, dimensions, shape, longitudinal and vertical position) and hydrostatic parameters (static trim angle, amount of added for...
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We discuss the covariant formulation of the dynamics of particles with abelian and non-abelian gauge charges in external fields. Using this formulation we develop an algorithm for the construction of constants of motion, which makes use of a generalization of the concept of Killing vectors and tensors in differential geometry. We apply the formalism to the motion of classical charges in abelian...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1985
ISSN: 0196-8858
DOI: 10.1016/0196-8858(85)90004-1