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Advanced Mathematics for Applications by Andrea Prosperetti

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6

Cylindrical Systems

6.1 Cylindrical coordinates

Cylindrical coordinates are generated by translating in the direction z normal to the (x, y) plane a system of plane polar coordinates (r, φ). Thus, the relation between the Cartesian coordinates (x, y, z) of a point x and its cylindrical coordinates (r, z, φ) are (see Figure 6.1)

image

(6.1.1)

The inverse relations are given in Table 6.1. The ranges of variation of the cylindrical coordinates are

image

(6.1.2)

The positions φ = 0 and φ = 2π are indistinguishable and φ is undefined ...

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