MAE345: 3-2-1 Euler Angles Visualization

Yaw-Pitch-Roll Gimbal Demo

Using standard 3-2-1 Euler angle convention: [BN] = T₁(φ) T₂(θ) T₃(ψ)

Yaw (ψ)
Pitch (θ)
Roll (φ)

Matrix Representation

\[ T_1(\phi) \]

\[ T_2(\theta) \]

\[ T_3(\psi) \]

\[ [BN] = T_1 T_2 T_3 \]

1	0	0
0
0

	0
0	1	0
	0

		0
		0
0	0	1

\[ = \]

NOTE: This uses the standard aerospace 3-2-1 Euler angle convention (Tait-Bryan angles Z-Y'-X''), also known as Yaw-Pitch-Roll.
DCM [BN] transforms vectors from Navigation (N) to Body (B) frame.
See Wikipedia for more details.

Animation Menu

Display Plane
Display Gimbals
Display Axes

	Yaw (ψ)	Pitch (θ)	Roll (φ)
Orientation 1
Orientation 2

Roll/Pitch/Yaw LERP
Quaternion SLERP

Directions

Manipulate the sliders to change yaw/pitch/roll. It is also possible to input your own angles and hit the "set" button to update them
For an animation which does linear interpolation between two sets of these angles, choose an initial yaw/pitch/roll next to "orientation1" in the animation menu to the right, as well as a final orientation next to "orientation 2." You can also automatically fill in the angles corresponding to the current slider positions by clicking "set from current."
Click the "animate" button to perform linear interpolation between orientation 1 and orientation 2
Click the "display gimbals" checkbox to toggle displaying of the gimbals. This may make it easier to view the animation
To view the gimbals from a different point of view, left click and drag your mouse. To zoom, scroll wheel. To translate, right click and drag

3-2-1 Euler Angle Convention

Rotation Order (DCM): [BN] = T₁(φ) T₂(θ) T₃(ψ) — Yaw (ψ) acts first, Roll (φ) acts last
Axis 3 (ψ): Yaw — rotation around Z-axis (body-down)
Axis 2 (θ): Pitch — rotation around Y-axis (lateral)
Axis 1 (φ): Roll — rotation around X-axis (forward/longitudinal)

This is the standard aerospace yaw-pitch-roll convention using intrinsic Z-Y'-X'' Tait-Bryan angles.

Credits

Created by: Liba Snyder
For: Dr. Bradley Darrall's Intermediate Dynamics course at University at Buffalo
Based on original project by: Chris Tralie
Modified to better align with typical Aerospace axes conventions.