Why are quaternions used for rotations?

Question

I\'m a physicist, and have been learning some programming, and have come across a lot of people using quaternions for rotations instead of writing things in matrix/vector fo

Answer 1

Gimbal lock is one reason, although as you say it is only a problem with Euler angles and is easily solvable. Euler angles are still used when memory is a concern as you only need to store 3 numbers.

For quaternions versus a 3x3 rotation matrix, the quaternion has the advantage in size (4 scalars vs. 9) and speed (quaternion multiplication is much faster than 3x3 matrix multiplication).

Note that all of these representations of rotations are used in practice. Euler angles use the least memory; matrices use more memory but don't suffer from Gimbal lock and have nice analytical properties; and quaternions strike a nice balance of both, being lightweight, but free from Gimbal lock.