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The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system. [1]They can also represent the orientation of a mobile frame of reference in physics or the orientation of a general basis in three dimensional linear algebra.
Denoted with the symbol Ω, it is the angle from a specified reference direction, called the origin of longitude, to the direction of the ascending node (☊), as measured in a specified reference plane. [1] The ascending node is the point where the orbit of the object passes through the plane of reference, as seen in the adjacent image.
The azimuth (or azimuthal angle) is the signed angle measured from the azimuth reference direction to the orthogonal projection of the radial line segment OP on the reference plane. The sign of the azimuth is determined by designating the rotation that is the positive sense of turning about the zenith. This choice is arbitrary, and is part of ...
In land navigation, azimuth is usually denoted alpha, α, and defined as a horizontal angle measured clockwise from a north base line or meridian. [5] [6] Azimuth has also been more generally defined as a horizontal angle measured clockwise from any fixed reference plane or easily established base direction line. [7] [8] [9]
Changing orientation of a rigid body is the same as rotating the axes of a reference frame attached to it.. In geometry, the orientation, attitude, bearing, direction, or angular position of an object – such as a line, plane or rigid body – is part of the description of how it is placed in the space it occupies. [1]
If the goal is to keep the shuttle during its orbits in a constant attitude with respect to the sky, e.g. in order to perform certain astronomical observations, the preferred reference is the inertial frame, and the RPY angle vector (0|0|0) describes an attitude then, where the shuttle's wings are kept permanently parallel to the Earth's ...
Geodetic latitude measures how close to the poles or equator a point is along a meridian, and is represented as an angle from −90° to +90°, where 0° is the equator. The geodetic latitude is the angle between the equatorial plane and a line that is normal to the reference ellipsoid.
the point's distance from a reference point called the pole, and; the point's direction from the pole relative to the direction of the polar axis, a ray drawn from the pole. The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth. [1]