Euler angle

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English

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Etymology

Named after Swiss mathematician Leonhard Euler (1707–1783).

Noun

Euler angle (plural Euler angles)

  1. (geometry) Any one of three angles which together describe the orientation of a rigid body with respect to a fixed three-dimensional coordinate system, according to a formalism introduced by Leonhard Euler.
    Euler angles can also represent the orientation of a mobile frame of reference in physics or the orientation of a basis in 3-dimensional linear algebra.
    • 1991, “AIAA Flight Simulation Technologies Conference: A Collection of Technical Papers”, in AIAA, page 271:
      The use of Euler angles or Quaternions to represent entity (i.e., vehicle) orientation in the draft military standard for Distributed Interactive Simulation has drawn fierce debate.
    • 2006, Don Koks, Explorations in Mathematical Physics: The Concepts Behind an Elegant Language, Springer, page 171:
      We have not drawn a picture, since Euler angle pictures of three-dimensional rotations are notoriously difficult to comprehend; what is very useful is for the reader to make a set of wire axes with labels to help follow the sequence of rotations.
    • 2008, Midori Kitagawa, Brian Windsor, MoCap for Artists: Workflow and Techniques for Motion Capture‎, Elsevier (Focal Press), page 188:
      Why do we need to know what Euler angles are? Because we use them. Many commercial 3D computer animation packages that are available today use Euler angles to describe and change orientations of objects.

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