Euler Angles

Define 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 the these angles.

Common uses for Euler angles include vehicle dynamics for aircraft, spacecraft, and automotive, as well as industrial automation and robotics equipment.

MATLAB^® and Simulink^® help simplify design problems that use Euler angles. For example, you can:

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

Examples and How To

• 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)

Software Reference

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

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