Why are quaternions used for rotations?

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.

Well I'm a physicist, too. And there are some situations where quaternions simply rock! Spherical Harmonics for example.

You have two atoms scattering, exchanging a electron. What's the orbital spin transfer? With quaternions it's just multiplication i.e.

Summing up the exponents of the SH base functions expressed as quaterions. (Getting the Legendre Polynomials into quaternion notation is a bit tedious though).

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