What it is
Translation is pure positional change. If every point on the aircraft moves the same distance in the same direction, the aircraft has translated — its orientation hasn't changed at all.
This is distinct from rotation, where the aircraft turns about an axis without its center necessarily moving.
The three translational directions
| Surge | Forward and backward — along the nose-to-tail (longitudinal) axis. This is what thrust and drag act on. |
| Sway | Left and right — along the wingtip-to-wingtip (lateral) axis. Crosswinds and sideslip create sway. |
| Heave | Up and down — along the vertical axis. The balance of lift and weight governs heave. |
In practice: pilots don't command surge, sway, or heave directly. They command roll, pitch, yaw, and throttle — the translational motion of the aircraft through space is a result of those inputs combined with the four forces.