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To define a spherical coordinate system, one must designate an origin point in space, O, and two orthogonal directions: the zenith reference direction and the azimuth reference direction. These choices determine a reference plane that is typically defined as containing the point of origin and the x– and y–axes , either of which may be ...
An azimuth (/ ˈ æ z ə m ə θ / ⓘ; from Arabic: اَلسُّمُوت, romanized: as-sumūt, lit. 'the directions') [1] is the horizontal angle from a cardinal direction, most commonly north, in a local or observer-centric spherical coordinate system.
Note: This page uses common physics notation for spherical coordinates, in which is the angle between the z axis and the radius vector connecting the origin to the point in question, while is the angle between the projection of the radius vector onto the x-y plane and the x axis. Several other definitions are in use, and so care must be taken ...
Azimuth is measured eastward from the north point (sometimes from the south point) of the horizon; altitude is the angle above the horizon. The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles of a spherical coordinate system: altitude and azimuth.
In many flight dynamics applications, the Earth frame is assumed to be inertial with a flat x E,y E-plane, though the Earth frame can also be considered a spherical coordinate system with origin at the center of the Earth. The other two reference frames are body-fixed, with origins moving along with the aircraft, typically at the center of gravity.
The spherical coordinate system is commonly used in physics. It assigns three numbers (known as coordinates) to every point in Euclidean space: radial distance r , polar angle θ ( theta ), and azimuthal angle φ ( phi ).
A point plotted using the spherical coordinate system. In spherical coordinates ( r , θ , φ ), r is the radial distance from the origin, θ is the zenith angle and φ is the azimuthal angle. In axisymmetric flow, with θ = 0 the rotational symmetry axis, the quantities describing the flow are again independent of the azimuth φ.
As is the case with spherical coordinates and spherical harmonics, Laplace's equation may be solved by the method of separation of variables to yield solutions in the form of oblate spheroidal harmonics, which are convenient to use when boundary conditions are defined on a surface with a constant oblate spheroidal coordinate.