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- W6628013 abstract "This chapter discusses curvilinear coordinates. The distinguishing feature of rectangular coordinates is that they permit a simple treatment of vector quantities. To ensure that vector components can be treated in a simple way, a curvilinear coordinate system should reduce to a rectangular system when a sufficiently small region is considered, and it must not reduce to a net of obliquely inclined lines. A net of lines intersecting at 90° constitutes an orthogonal coordinate system. A complex number is an ordered pair of real numbers, but additionally, these numbers can be considered as components of a vector in an orthogonal coordinate system. This is what is conveyed by the term conformal transformation, and it ensures that rectangular coordinate lines in the ξ-plane transform into a set of orthogonal coordinate lines in the z-plane, though in general, lines will be curved. It appears that any differentiable function of ξ may be used for generating an orthogonal system of coordinate lines in the physical plane. Any body can then be superimposed on this plane for the purpose of specifying positions of points on the body." @default.
- W6628013 created "2016-06-24" @default.
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- W6628013 date "1968-01-01" @default.
- W6628013 modified "2023-09-27" @default.
- W6628013 title "CURVILINEAR COORDINATES" @default.
- W6628013 doi "https://doi.org/10.1016/b978-0-08-203495-7.50008-x" @default.
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