Euler Angles

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Define the orientation of a body in three-dimensional space

Euler angles are a method of determining the rotation of a body in a given coordinate frame. They can be defined as three rotations relative to the three major axes. Euler angles are most commonly represented as phi for x-axis rotation, theta for y-axis rotation and psi for z-axis rotation. Any orientation can be described by using a combination of these angles.

Euler angles are often used in the development of vehicle dynamics for aircraft, spacecraft, and automotive, as well as industrial automation and robotics equipment.

Common tasks for simplifying design problems that use Euler angles include:

  • Transforming coordinate systems in real-time simulation or post processing of data
  • Visualizing Euler angles and flight data in FlightGear flight simulator
  • Using functions to transform between quaternions and Euler angles

For details on performing these tasks, see MATLAB® and Simulink®.

Examples and How To

Software Reference

See also: quaternion, linearization, numerical analysis, design optimization, real-time simulation, Monte Carlo simulation, model-based testing