ABSTRACT
Cartesian or rectangular
(
x
,
x
). A point
p
can be located either by the angle
θ
, measured from the reference direction
x
, and range
r
from the reference point 0, or by its two distances from two perpendicular axes,
x
,
x
. The relationships between the two systems are given by
(53.1)
(53.2)
Figure 53.2 shows two systems of three-dimensional coordinates:
spherical
(
α, β,
r
)
and Cartesian or rectangular (
x
,
x
,
x
). The Cartesian system depicted in Fig. 53.2 is
right-handed
, since a right-threaded screw rotated by an angle less than 90˚ from +
x
to +
x
would advance in the direction of +
x
. The relations between these two systems are as follows:
x1 r θcos=
x2 r θsin=
θ tan 1-x2 x1⁄( )=
(53.3)
(53.4)
One example of spherical coordinates consists of latitude
φ
, longitude
λ
, and earth radius
R
, when the earth is considered as a sphere. A more accurate representation of the earth is an ellipsoid of revolution about its minor (shorter) axis. Coordinates referring to the earth ellipsoid, and other figures, are given in Chapter 55, “Geodesy.”
