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  2. Spherical coordinate system - Wikipedia

    en.wikipedia.org/wiki/Spherical_coordinate_system

    And these systems of the mathematics convention may measure the azimuthal angle counterclockwise (i.e., from the south direction x-axis, or 180°, towards the east direction y-axis, or +90°)—rather than measure clockwise (i.e., from the north direction x-axis, or 0°, towards the east direction y-axis, or +90°), as done in the horizontal ...

  3. Horizontal coordinate system - Wikipedia

    en.wikipedia.org/wiki/Horizontal_coordinate_system

    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. Therefore, the horizontal coordinate system is sometimes called the az/el system, [1] the alt/az system, or the alt-azimuth system, among

  4. Axis–angle representation - Wikipedia

    en.wikipedia.org/wiki/Axisangle_representation

    The angle θ and axis unit vector e define a rotation, concisely represented by the rotation vector θe.. In mathematics, the axisangle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the ...

  5. Rotation formalisms in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotation_formalisms_in...

    The angle θ which appears in the eigenvalue expression corresponds to the angle of the Euler axis and angle representation. The eigenvector corresponding to the eigenvalue of 1 is the accompanying Euler axis, since the axis is the only (nonzero) vector which remains unchanged by left-multiplying (rotating) it with the rotation matrix.

  6. Euler's rotation theorem - Wikipedia

    en.wikipedia.org/wiki/Euler's_rotation_theorem

    A spatial rotation is a linear map in one-to-one correspondence with a 3 × 3 rotation matrix R that transforms a coordinate vector x into X, that is Rx = X. Therefore, another version of Euler's theorem is that for every rotation R , there is a nonzero vector n for which Rn = n ; this is exactly the claim that n is an eigenvector of R ...

  7. Quaternions and spatial rotation - Wikipedia

    en.wikipedia.org/wiki/Quaternions_and_spatial...

    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]

  8. Azimuth - Wikipedia

    en.wikipedia.org/wiki/Azimuth

    Normal-section azimuth is the angle measured at our viewpoint by a theodolite whose axis is perpendicular to the surface of the spheroid; geodetic azimuth (or geodesic azimuth) is the angle between north and the ellipsoidal geodesic (the shortest path on the surface of the spheroid from our viewpoint to Point 2).

  9. Altitude - Wikipedia

    en.wikipedia.org/wiki/Altitude

    The stratosphere is also the altitude limit of jet aircraft and weather balloons, as the air density there is roughly 1 ⁄ 1000 of that in the troposphere. [1] Vertical distance comparison The term altitude can have several meanings, and is always qualified by explicitly adding a modifier (e.g. "true altitude"), or implicitly through the ...