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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
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 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.
References and notes
- ^ Edmund Taylor Whittaker (1988). A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Reprint of fourth edition of 1936 with foreword by William McCrea ed.). Cambridge University Press. p. 1. ISBN 0521358833. http://books.google.com/books?id=epH1hCB7N2MC&pg=PA4&dq=rigid+bodies+translation&lr=&as_brr=0&sig=ACfU3U35vNtLy6utF2QKzYa82mGSyp_jYw#PPA1,M1.
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