Euler Angles and their use in Aerospace

How do you specify the orientation of a three dimensional object. Lets imagine a piece of square block placed on a flat table. Let us define this as initial position and mark it as (x,y,z). Now slightly tilt the box around Z axis. i.e. rotate it by not changing the sides.

Video Credits: Greg Horn

So now the new position of the block be mentioned as (X,Y,Z) when we see the block we can observe an angle change in x and y axis and no change in z axis. Just take note of the angles in a piece of paper and give it to your friend...

Now just by knowing the co-ordinate values can he position the square block in the same way you did? Of course he can!

In case of an aircraft, there are 6 degrees of freedom. Few data such as position, orientation and heading of the aircraft needs to be known to navigate to the target. So how to describe the orientation in simple and accurate manner?

 

Video Credits: Udacity

Euler did had a way to solve this issue. He introduced three angles φ, θ, ψ or α, β, γ to describe the orientation of a three dimensional body with respect to a fixed co-ordinate system. Euler angles are used to denote the yaw pitch, roll, heading, elevation, and bank of an aircraft, which are the major factors of an aircraft. Euler angles are also used in sensors and flight simulators, etc. which helps flight navigate.

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