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Calculus Of Moving Surfaces
The calculus of moving surfaces (CMS) is an extension of the classical tensor calculus to deforming manifolds. Central to the CMS is the Tensorial Time Derivative \dot whose original definition J. Hadamard, Leçons Sur La Propagation Des Ondes Et Les Équations de l'Hydrodynamique. Paris: Hermann, 1903. was put forth by Jacques Hadamard. It plays the role analogous to that of the covariant derivative \nabla _ on differential manifolds in that it produces a tensor when applied to a tensor. Suppose that \Sigma_t is the evolution of the surface \Sigma indexed by a time-like parameter t. The definitions of the surface velocity C and the operator \dot are the geometric foundations of the CMS. The velocity C is the rate of deformation of the surface \Sigma in the instantaneous normal direction. The value of C at a point P is defined as the limit : C=\lim_ \frac where P^ is the point on \Sigma_ that lies on the straight line perpendicular to \Sigma_ at point P. This definitio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dannebrog
Dannebrog (until the mid-20th century often spelled Danebrog) may refer to: Flags and orders * The national Flag of Denmark * Order of the Dannebrog ( da, Dannebrogordenen, links=no), a Royal Danish decoration Places * Dannebrog Island, an island in Greenland * Dannebrog Islands, an island group in Antarctica * Dannebrog, Nebraska, a village in Nebraska, United States Ships * Danish ironclad Dannebrog, Danish ironclad ''Dannebrog'', a frigate of the Royal Danish Navy, also known as the HDMS ''Dannebrog'' (1850) * HDMS Dannebroge, HDMS ''Dannebroge'' (1692) (The name is spelled Dannebrog in some references) * HDMY Dannebrog (1879), HDMY ''Dannebrog'' (1879), the first royal Danish side-wheel paddle steam-yacht, named after the flag * HDMY Dannebrog (A540), HDMY ''Dannebrog'' (A540), a Danish royal yacht, named after the flag {{disambiguation, geo, ship ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
