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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 3-dimensional linear algebra.
The azimuth is the angle between the north vector and the star's vector on the horizontal plane. [ 2 ] Azimuth is usually measured in degrees (°), in the positive range 0° to 360° or in the signed range -180° to +180°. The concept is used in navigation, astronomy, engineering, mapping, mining, and ballistics.
The polar angle may be called inclination angle, zenith angle, normal angle, or the colatitude. The user may choose to ignore the inclination angle and use the elevation angle instead, which is measured upward between the reference plane and the radial line—i.e., from the reference plane upward (towards to the positive z-axis) to the radial line.
In geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion. The orientation of an object at a given instant is ...
The various Euler angles relating the three reference frames are important to flight dynamics. Many Euler angle conventions exist, but all of the rotation sequences presented below use the z-y'-x" convention. This convention corresponds to a type of Tait-Bryan angles, which are commonly referred to as Euler angles. This convention is described ...
3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]
Rotation matrix. In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix. rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system.
t. e. A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. (This article considers only frames rotating about a fixed axis. For more general rotations, see Euler angles.)
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