Equivalence of quaternion rotation

Compute rotated point (via quaternions)

pp = {x, y, z} ; k = {kx, ky, kz} ; p1 = Cos[θ] pp + Sin[θ] Cross[k, pp] + (1 - Cos[θ]) (k . pp) k //ExpandAll ; p1 // Nice

( 2 2 ... - kx x cos(θ) kz - ky y cos(θ) kz + z cos(θ) - ky x sin(θ) + kx y sin(θ)

Compute rotated point (via equivalent angle-axis rotation matrix)

p2 = rk4 . pp // ExpandAll ; p2 // Nice

( 2 2 ... - kx x cos(θ) kz - ky y cos(θ) kz + z cos(θ) - ky x sin(θ) + kx y sin(θ)

Check that they are equivalent

p1 == p2

True

Created by Mathematica  (September 7, 2003)