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I started to study Roy Featherstone's book "Rigid Body Dynamics Algorythms".

The book starts off by explaining Spatial Algebra, where translations and rotations are gathered in a 6-D vector using Plucker's coordinates.

At some point the book says;

"A line vector is a quantity that is characterized by a directed line and a magnitude.

A pure rotation of a rigid body is a line vector, and so is a linear force

acting on a rigid body. A free vector is a quantity that can be characterized by

a magnitude and a direction. Pure translations of a rigid body are free vectors,

and so are pure couples. A line vector can be specified by five numbers, and

a free vector by three. A line vector can also be specified by a free vector and

any one point on the line."

Can someone explain the difference between line vector and free vector in different words, especially the part where a line vector can be specified by five numbers.

my current understanding would be that a free vector is the common euclidean vector, but then in the formulation above the two seem to differ by the fact that one is characterized by a directed line and the other by a direction. What's the difference ?

Disclaimer; most of my algebra is self taught so if say some non-sense, that's why :)

Hopefully this is the right location for such a post.

Michael

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# Difference between line vector and free vector

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