Translation (physics)

# Translation (physics)

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Encyclopedia
In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, translation (Translational motion) is movement that changes the position
Displacement (vector)
A displacement is the shortest distance from the initial to the final position of a point P. Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P...

of an object, as opposed to rotation
Rotation
A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...

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

where is the same vector for each point of the object. The translation vector common to all points of the object describes a particular type of displacement
Displacement (vector)
A displacement is the shortest distance from the initial to the final position of a point P. Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P...

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
Fixed point (mathematics)
In mathematics, a fixed point of a function is a point that is mapped to itself by the function. A set of fixed points is sometimes called a fixed set...

.