Euler angles

Understanding Euler Angles

Have you ever wondered how airplanes, robots, or video game characters rotate? They use something called Euler angles! Let's explore what they are and why they are important.

What Are Euler Angles?

Euler angles are three numbers that describe how an object rotates in 3D space. Imagine a toy airplane. You can turn it in three different ways:

Roll – Rotating around the front-to-back axis (like tilting your head sideways).

Pitch – Rotating around the side-to-side axis (like nodding your head "yes").

Yaw – Rotating around the up-and-down axis (like shaking your head "no").

By combining these three rotations in a specific order, we can describe any orientation an object can have!

How Do They Work?

Imagine you are holding a book. If you first tilt it forward (pitch), then turn it sideways (yaw), and finally roll it, you will get a completely different final position compared to changing the order of rotations. That’s why the sequence of rotations matters when using Euler angles.

Scientists and engineers use Euler angles to:

Control airplanes and spacecraft

Animate characters in video games

Move robots accurately

Design virtual reality experiences

Gimbal Lock – A Problem with Euler Angles

One issue with Euler angles is gimbal lock. This happens when two rotation axes line up, making one rotation ineffective. Imagine if you tilt your head so much that "yaw" and "roll" do the same thing—it limits movement! Because of this, some engineers prefer other methods, like quaternions, for smooth rotations.

Conclusion

Euler angles are a simple and powerful way to describe rotations in 3D. They are used in many fields, from engineering to entertainment. Understanding them helps us see how things move in the world around us!