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What is the mathematical definition of sliding vectors and their operations, as used in mechanics? What kind of mathematical structure do they form? Does the operation of constructing the "space" of sliding vector of an affine space has a name?

An example of a sliding vector, as i understand it, is a force applied to a point of a rigid body. The effect of the force will remain the same if the point of application is "slid" along the line of application.

If two sliding vectors are coplanar, their sum is almost always a sliding vector, unless the two vectors are parallel, opposite, of the same magnitude, but supported by different parallel lines.

The straightforward definition of the "space" of sliding vectors that comes to my mind is that it is the quotient of the abelian group freely generated by all pairs of points of the given affine space modulo the necessary relations. This looks a bit awkward to me. The name "space of sliding vectors" does not fit well too, because it contains certain sums which are not sliding vectors.

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