How Euler Angles Work

Transcript

Oiler angles break down a complex rotation into three simple chain rotations about the axis of the cube to represent any 3D orientation. Let's look at this cube. This cube has three axes, the X, Y, and Z axis. This cube starts out oriented with the world reference frame X, Y, and Z. To model this rotation, we will follow a Z YX rotation sequence.

First, we rotate the cube about the Z-axis by some angle S. When we do this, notice that the x and y axis of the cube have been rotated by s, creating a new local axis x prime and yp prime. We then move on to our second rotation. This time we rotate the cube about this new yp prime axis by an angle theta. This rotation rotates our z and x- prime axes, creating a new zprime and x-prime axis.

Finally, we rotate the cube about the new xp prime axis by an angle phi. This rotation rotates the Z-prime and Yprime axes to become our new final XP prime, YP prime, and Zprime axes. We now have represented our final orientation by breaking one complex rotation into three simple rotations with three angles.