The general displacement of a rigid body (or coordinate frame) with one point fixed is a rotation about some axis. Furthermore, a rotation may be described in any basis using three angles.
Euler's Displacement Theorem
See also
Euclidean Motion, Euler Angles, Rigid Motion, Rotation, TranslationExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Euler's Displacement Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EulersDisplacementTheorem.html