# curvilinear

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## curvilinear

(kĕr′vĕ-lĭn″ē-ăr)
Concerning or pert. to a curved line.
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References in periodicals archive ?
We introduce an orthogonal curvilinear coordinate system
Symbol [partial derivative] indicates the partial derivatives; the parametric coefficients for shells, with constant radii of curvature, that use the orthogonal curvilinear coordinate system are
Using tensor analysis, which is extremely useful especially for three-dimensional problems in any curvilinear coordinate system, a number of researchers, including Fung , Green and Zerna  have developed the general theory of elasticity.
This paper introduces the solution of the Poisson problem in a certain type of curvilinear coordinate domain and points out problems with it.
Equation 13 provides an elegant general formulation of the equation of virtual work in curvilinear coordinates. At this stage, the virtual displacements need not be compatible with the essential boundary conditions defined on S.
This geometry, defined by metric tensor [g.sub.ij], suggests to identify local bases (11) and (13), intrinsically related to the physical properties of medium, with (22) and (23) of the just described arbitrary curvilinear coordinates system.
He explains the action approach, including its relation to Maxwell's equation and Dirac fields, then examines continuous symmetries and conservation laws, magnetostatics, multivalued fields in superfluids and superconductors, magnetic monopoles, electric charge confinement, multivalued mapping from ideal crystals to crystals with defects, defect melting, relativistic mechanics in curvilinear coordinates, torsion and curvature from defects and embedding, mutivalued mapping, field equations of gravitation, fields of integer spin, particles with half-integer spins, covariant conservation gravitation of spinning matter as a gauge theory, evanescent properties of torsion in gravity, the teleparallel theory of gravitation embedding, and emerging gravity.
A finite element method is developed from application of the principle of virtual work for the beam written in curvilinear coordinates in order to include the effects of finite deformation.
After presenting the foundations in a form free from any coordinate system, the author follows with a chapter on the technique of writing Navier-Stokes equations and Euler's equations in general steady and nonsteady curvilinear coordinates, as well as the essential aspects of vorticity and stream functions.

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