This came as a surprise to me. I am 99.99% certain the
notion of "bound vector" does not appear in any of my math
books. I don't recall seeing it in any of my physics books.
I don't recall hearing any physicist utter the term or use
the concept.
The concept of "bound vector" definitely exists in the minds
of students, even if they don't can't give a name to it.
In particular, I call attention to the idea of expressing
Newton's third law in terms of bound vectors. I'm not saying
this is a /good/ idea, but it's not completely crazy.
One problem with bound vectors is that they are incompatible
with the mathematical definitions of vector and vector space.
And as far as I can tell, the tradition within physics for
at least the last 50 years is to stick with the mathematical
definition of vector and vector space, i.e. to use "free"
vectors for everything. In particular, in Newton's laws,
the force and the point of application are two different
vectors. To quantify the third law, it suffices to assert
conservation of the bivector r/\p (angular momentum). Then
conservation of the vector p (momentum) is obtained as a
corollary, as you can see by choosing a far-far-away datum
(origin) for defining the lever arm (r).
However ... I would like to throw this open as a question to
the group.
-- Can anybody cite an example of "bound vectors" appearing
in a reputable physics text?
-- As a matter of policy going forward, is there any advantage
to introducing "bound vectors" into the physics curriculum, or
should should stick with the mathematicians' definitions of
vector and vector space?