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Euler angles (in 3-2-1 sequence) to quaternion conversion. By combining the quaternion representations of the Euler rotations we get for the Body 3-2-1 sequence, where the airplane first does yaw (Body-Z) turn during taxiing onto the runway, then pitches (Body-Y) during take-off, and finally rolls (Body-X) in the air.
Geographic coordinate conversion has applications in cartography, surveying, navigation and geographic information systems. In geodesy, geographic coordinate conversion is defined as translation among different coordinate formats or map projections all referenced to the same geodetic datum. [1] A geographic coordinate transformation is a ...
The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper degree of "tilt ...
The nautical mile (nmi) was originally defined as the arc length of a minute of latitude on a spherical Earth, so the actual Earth's circumference is very near 21 600 nmi. A minute of arc is π 10 800 of a radian. A second of arc, arcsecond (arcsec), or arc second, denoted by the symbol ″, [2] is 1 60 of an arcminute, 1 3600 ...
the plane pitch axis is on axis y of the reference frame; the plane yaw axis is on axis z of the reference frame; The rotations are applied in order yaw, pitch and roll. In these conditions, the Heading (angle on the horizontal plane) will be equal to the yaw applied, and the Elevation will be equal to the pitch.
In blue, the point (4, 210°). In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ...
Angles in the hours ( h), minutes ( m), and seconds ( s) of time measure must be converted to decimal degrees or radians before calculations are performed. 1 h = 15°; 1 m = 15′; 1 s = 15″ Angles greater than 360° (2 π ) or less than 0° may need to be reduced to the range 0°−360° (0–2 π ) depending upon the particular calculating ...
t. e. A geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on Earth as latitude and longitude. [1] It is the simplest, oldest and most widely used of the various spatial reference systems that are in use, and forms the basis for most others.