Translation (physics)

In physics, translation (Translational motion) is movement that changes the position of an object, as opposed to rotation. For example, according to Whittaker:

If a body is moved from one position to another, and if the lines joining the initial and final points of each of the points of the body are a set of parallel straight lines of length ℓ, so that the orientation of the body in space is unaltered, the displacement is called a translation parallel to the direction of the lines, through a distance ℓ.

— E.T. Whittaker: A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, p. 1

A translation is the operation changing the positions of all points (x, y, z) of an object according to the formula

$(x,y,z) \to (x+\Delta x,y+\Delta y, z+\Delta z)$

where $(\ \Delta x,\ \Delta y,\ \Delta z)$ is the same vector for each point of the object. The translation vector $(\ \Delta x,\ \Delta y,\ \Delta z)$ common to all points of the object describes a particular type of displacement of the object, usually called a linear displacement to distinguish it from displacements involving rotation, called angular displacements.

A translation of space (or time) should not be confused with a translation of an object. Such translations have no fixed points.

See also

• Translation (geometry)