# What are the 3 Euler angles?

I am currently reading up on inertial measurement in aircraft systems. Euler angles are one of the concepts I am a bit confused with. In an Euler angle-rate matrix there seem to be 3 parameters: p, q, and r. From what I understand about this we are talking about 3 values that each represent the rotation around an axis with reference to a base/mount.

My question is, does each of the parameters p, q, and r represent a particular axis? If so, what do each of the parameters represent (in terms of either x, y, and z or pitch, roll, and yaw)?

Here are some references to what I've been reading through:

Aircraft Equations of Motion

Attitude Representation

• Do you mean angle-rate matrix or rotational matrix? Euler angles are typically denoted as α, β, γ, or φ, θ, ψ. Different authors may use different sets of rotation axes to define Euler angles, or different names for the same angles. Therefore, any discussion employing Euler angles should always be preceded by their definition. Check your source for their defintion. – JMLCarter Oct 3 '17 at 1:39
• @JMLCarter The body-axis angular rate vector, denoted as p, q, r. – Snoop Oct 3 '17 at 12:13
• OK, so it's the time differential of your Euler angles. That still doesn't inform the initial/zero direction, sense (clockwise, anti-clockwise) and limits of each of the three Euler angles. – JMLCarter Oct 3 '17 at 12:17
• @JMLCarter Not quite sure I understand. – Snoop Oct 3 '17 at 12:40
• roll, pitch and yaw, as explained here en.wikipedia.org/wiki/Euler_angles – JMLCarter Oct 3 '17 at 13:56