Re: [Phys-l] bound vectors ... or not

[John Mallinckrodt <ajm@csupomona.edu>]

I don't see any advantage, much less any necessity, but I *do* see  
much potential for needless confusion in trying to distinguish  
between "bound" and "free" vectors.  Vectors have magnitude and  
direction.  They do not have "location."  The standard "position  
vector" locates a specific point in space relative to some origin by  
having a magnitude and a direction such that, *if* its tail is  
positioned at the origin, its tip will be at the desired point.

Am I missing something?

John Mallinckrodt
Cal Poly Pomona

On Sep 5, 2010, at 9:59 PM, Stefan Jeglinski wrote:

> I'm confused about this discussion too...
>
> > 2) I think we all agree that in many situations when dealing
> > with a force, we need the idea of direction-and-magnitude of
> > the force and also the idea of point-of-application .....
>
> Agreed. And to your point about viewing the angular momentum L as
> (d/dt) of the torque T, I would expect what follows below to apply to
> both L = r x p and T = r x F.
>
>
> > The question is simply whether we want to express those two
> > things using one "vector" (i.e. a so-called bound vector)
> > or using two vectors (i.e. plain old vectors, aka free
> > vectors).
>
> Eh? Based on the wiki article you cited, a bound vector "possesses a
> definite initial point and terminal point." By this simple reading,
> both r and F qualify. Specifically, T is context-sensitive... I can
> make it zero simply by defining the vector r appropriately wrt F,
> which definitely qualifies r as a bound vector. Likewise F: changing
> the direction and location (initial and terminal points) of F will
> change the torque for a specified r. The torque vector T, on the
> other hand, would suddenly seem to qualify as the free vector. Once r
> and F are specified completely, each with their initial and terminal
> points, the vector T (direction determined by right-hand rule,
> magnitude by rFsin(theta)), is more like a disembodied entity, aka
> free vector. Likewise the discussion for L = r x p: {r,p} = bound, L
> = free.
>
>
> > My reading of the math and physics literature going back 50+
> > years is that vector means free vector exclusively, so that
> > a so-called "bound vector" is not really a vector at all, but
> > rather a pair of vectors, like two persons inside a horse
> > costume.
>
> Are you saying that you would view r x F as one bound vector
> consisting of a pair of free vectors r and F? By my reading, it is
> exactly the opposite. However, back to my original admission of
> confusion - what purpose is there to begin with to define bound and
> free? I [either sheepishly or sadly, not sure which] never heard of a
> bound vector until this discussion. Does it satisfy someone's need to
> formalize this stuff to the nth degree, or does it serve a useful
> purpose?
>
>
> > I'm sure Banesh Hoffmann didn't write about bound vectors on
> > a whim.
>
> I don't have Hoffmann's book so I can't comment. As to the bivector,
> I obviously have access to your Clifford pages now that your server
> is back up, but can't say I've read through it enough to answer your
> bivector hypothesis.
>
>
> Stefan Jeglinski
>
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