what does represent quaternions addition?

[luzop]

I know that if q1 and q2 indicate rotations, then q2q1
represents the composite rotation of q1 followed by q2.

but what about addition?

[Noor]

I believe quaternion addition is similar to vector space translation (in 4D), but have no geometric meaning.

[davepermen]

depends on what you use the quaternions for. quaternions with only imaginary part can be used to represent vectors, and then, quaternion addition results in vector concatenation, a.k.a. translation.

[luzop]

Thanks