Results 201 to 210 of about 37,597 (261)

Orthogonal Curvilinear Coordinates

The Mathematical Gazette, 1966
Although the gradient of a scalar, and the curl and divergence of a vector can be obtained by various elementary methods in terms of curvilinear components and coordinate vectors, the corresponding results for the components of strain and the vector divergence of stress are usually obtained by specializing the formulae for covariant derivatives.
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Curvilinear coordinates

2018
Abstract This chapter presents a discussion on curvilinear coordinates in line with the introduction on Cartesian coordinates in Chapter 1. First, the chapter introduces a new system C of curvilinear coordinates xⁱ = xⁱ(Xj) (also sometimes referred to as Gaussian coordinates), which are nonlinearly related to Cartesian coordinates.
Nathalie Deruelle, Jean-Philippe Uzan
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ON KORN'S INEQUALITIES IN CURVILINEAR COORDINATES

Mathematical Models and Methods in Applied Sciences, 2001
We show how the inequality of Korn's type on a surface can be established as a corollary to the three-dimensional Korn inequality in curvilinear coordinates. The proof relies in particular on a careful study of the linearized Kirchhoff–Love displacement fields inside a "shell-like" body.
Ciarlet, Philippe G., Mardare, Sorin
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Curvilinear Coordinates

Abstract Discusses general coordinates for 3D space, and the geometry of coordinate curves and surfaces. Introduces Jacobian matrices and determinants, tangents and normals bases, that become the covariant and contravariant bases. Formula specific to general orthogonal coordinates are also derived.
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Generalised Curvilinear Coordinates

1992
The computation of flowfields in and around complex shapes such as ducts, engine intakes, complete aircraft or automobiles, etc., involves computational boundaries that do not coincide with coordinate lines in physical space. For finite difference methods, the imposition of boundary conditions for such problems has required a complicated interpolation ...
Karkenahalli Srinivas, Clive A. J. Fletcher   +1 more
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Quantization in curvilinear coordinates

International Journal of Theoretical Physics, 1990
Two prescriptions often used to find Hermitian operators corresponding to classical quantities can be removed. Components of momentum are of three types, linear momentumP〈q〉k canonical momentumP(q)k and generalized momentumPqk. Using metrical geometry, their mutual relations are established. The operatorsP〈q〉k andP(q)k are given by substituting quantum
Lee Ting Hsang, An Chong Shan, Zhai Tian Yi   +2 more
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Hydrodynamics in curvilinear coordinates

Acta Physica Hungarica, 1987
We consider the hydrodynamics in curvilinear comoving coordinates and present the equations governing the motion of a fluid with viscosity (and, in part, with heat conductivity). The underlying symmetry is spherical or planar. The Lagrangian form of the equations is suitable for numerically treating such problems as stellar collapse, neutron star ...
B. Kämpfer, B. Lukács
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Curvilinear Coordinate Systems

1989
If three single-valued scalar point functions u, v and w are defined throughout a region of space R, and have level surfaces (u = constant, v = constant, w = constant) which nowhere meet in a common curve or coincide, then we may associate with each point of R a triplet of values known as its curvilinear coordinates.
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Curvilinear Coordinate Systems

1993
Shells involve thin walled elastic bodies wherein one dimension is considerably smaller than the other two, but in which the midsurface is curved in at least one direction. Thus, to describe a shell succinctly, curvilinear coordinates must be employed. This causes considerable complications in the mathematical descriptions and operations, not existing ...
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Curvilinear Coordinates, Local Coordinate Transformations

2019
The reader probably has experience in using polar coordinates on the 2D plane, or spherical coordinates in the 3D space. Below, we consider a general treatment of curvilinear coordinate systems, which include these and many other examples.
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