# Euler Angles for Space Shuttle

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The Euler (or Eulerian) angles, usually designated , , and , uniquely determine the orientation of a rigid body in three-dimensional space. There are several conflicting conventions for defining the Euler angles, depending on the choice of axes and the order in which rotations about these axes are performed. This Demonstration uses the convention described in *MathWorld*, hyperlinked below in Related Links. This is most commonly used in physics and is known as the " convention." For topical relevance, NASA's space shuttle is chosen as the rigid body. The angles and are analogous to the spherical polar coordinates orienting the main axis of the shuttle, while describes rotation about this axis. The ranges of the three Euler angles are given by: , , and . The corresponding motions of a rigid body are termed nutation, precession and intrinsic rotation.

Contributed by: S. M. Blinder (March 2011)

With a correction by Joeri Gerlo, University of Ghent

Open content licensed under CC BY-NC-SA

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"Euler Angles for Space Shuttle"

http://demonstrations.wolfram.com/EulerAnglesForSpaceShuttle/

Wolfram Demonstrations Project

Published: March 7 2011