Spherical Coordinates

spherical coordinates

[′sfir·ə·kəl kō′ȯrd·ən·əts] (mathematics) A system of curvilinear coordinates in which the position of a point in space is designated by its distance r from the origin or pole, called the radius vector, the angle φ between the radius vector and a vertically directed polar axis, called the cone angle or colatitude, and the angle θ between the plane of φ and a fixed meridian plane through the polar axis, called the polar angle or longitude. Also known as spherical polar coordinates.

Spherical Coordinates

The spherical coordinates of a point M are the three numbers r, θ, and ɸ. These numbers are defined relative to three mutually perpendicular axes, which are called the x-axis, y-axis, and z-axis and intersect at the point O (Figure 1). The number r is the distance from O to M. The number θ is the angle between the vector and the positive direction of the r-axis. The number ɸ is the angle through which the positive half of the x-axis must be turned counterclockwise so that it coincides with the vector where N is the projection of M on the ry-plane. The spherical coordinates of M thus depend on the choice of O and the three axes. The relations between the spherical and Cartesian coordinates are given by the following equations:

x = r sin θ cos ɸ

y = r sin θ cos ɸ

z = r cos θ

Figure 1

Spherical coordinates are widely used in mathematics and in applications of mathematics to physics and engineering.

单词	spherical coordinates
释义	spherical coordinates spherical coordinates pl n (Mathematics) three coordinates that define the location of a point in three-dimensional space in terms of the length r of its radius vector, the angle, θ, which this vector makes with one axis, and the angle, φ, made by a second axis, perpendicular to the first, with the plane containing the first axis and the point. Usually written (r, θ, φ) Translations coordinate sferiche Spherical Coordinates spherical coordinates [′sfir·ə·kəl kō′ȯrd·ən·əts] (mathematics) A system of curvilinear coordinates in which the position of a point in space is designated by its distance r from the origin or pole, called the radius vector, the angle φ between the radius vector and a vertically directed polar axis, called the cone angle or colatitude, and the angle θ between the plane of φ and a fixed meridian plane through the polar axis, called the polar angle or longitude. Also known as spherical polar coordinates. Spherical Coordinates The spherical coordinates of a point M are the three numbers r, θ, and ɸ. These numbers are defined relative to three mutually perpendicular axes, which are called the x-axis, y-axis, and z-axis and intersect at the point O (Figure 1). The number r is the distance from O to M. The number θ is the angle between the vector and the positive direction of the r-axis. The number ɸ is the angle through which the positive half of the x-axis must be turned counterclockwise so that it coincides with the vector where N is the projection of M on the ry-plane. The spherical coordinates of M thus depend on the choice of O and the three axes. The relations between the spherical and Cartesian coordinates are given by the following equations: x = r sin θ cos ɸ y = r sin θ cos ɸ z = r cos θ Figure 1 Spherical coordinates are widely used in mathematics and in applications of mathematics to physics and engineering.
随便看	whangarei whangarei, new zealand whangarei (town) whangdoodle whanged whangee whanghee whanging whangpoo whangs whangster whangydoodle whank whank off whankster whao whap whapped whapper whapping whaps whaqs wharc whare wharenui