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^{®}.

- Accelerating Flight Vehicle Design (Article)
- Displaying Flight Trajectory Data (Example)
- Converting Units and Transforming Coordinate Systems (Aerospace Toolbox)
- Axes Transformation in Simulink (Aerospace Blockset)
- Gulfstream Develops Flight Simulator (User Story)
- Processing Large Telemetry Data Sets for Biomechanical Performance Analysis (Article)

- Aerospace Toolbox (Product)
- Aerospace Blockset (Product)
- Working with the Flight Simulator Interface (Documentation)
- Connect Model to FlightGear Flight Simulator (Documentation)
- Create Directional Cosine Matrix from Rotation Angles (Function)
- Convert Quaternion to Rotation Angles (Function)

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