Euler angles

Euler angles are a way to describe which way an object is pointing using just three numbers. Instead of giving the full math of an orientation all at once, you build it up from three simple spins, one after another, each around one axis. The most common version in robotics is roll, pitch, and yaw. Picture an airplane: roll is the wing-dipping twist about the direction of travel, pitch is the nose tilting up or down, and yaw is the nose swinging left or right. Apply those three turns in order and you can aim the plane any direction you like.

The catch is that order matters and you must agree on it. Rolling first and then yawing leaves you facing somewhere different than yawing first and then rolling, because each spin happens around the axes left by the previous spins. So Euler angles only mean something once everyone fixes a convention, such as 'yaw, then pitch, then roll.' People love Euler angles because three numbers are easy to read, type, and show on a dashboard, and each one matches an intuition a human already has. But they hide a famous trap: at certain orientations two of the three spins line up and start doing the same job, a failure called gimbal lock, which is why robots often convert them to a rotation matrix or a quaternion for the actual computing.