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

["LaMontagne, Bob" <RLAMONT@providence.edu>]

This definition comes from Answers.com:

"(mechanics) A vector whose line of application and point of application are both prescribed, in addition to its direction." 

and a discussion on physics forums appears to agree with this

http://www.physicsforums.com/showthread.php?t=391465

The wiki definition seems consistent with this if the tail of the vector defines a point of application and the head defines the line of application and the direction.

I am interested to see where this thread leads because many general physics texts (Knight, for example) carefully define vectors to have only length and direction and then later the term "point of application" is introduced without rationalization with the previous definition.

Bob at PC

________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker [jsd@av8n.com]
Sent: Sunday, September 05, 2010 7:10 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] bound vectors ... or not

On 09/05/2010 02:58 PM, LaMontagne, Bob wrote:

> At first blush it appears that the concept of a bound vector is not
> required for angular momentum, but it is useful for torque.

Lost me there.


1) Since
  torque = (d/dt) angular momentum
it would seem to me that whatever is required or useful for
torque is equally required or useful for angular momentum
... and vice versa.


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 .....
That's not the question.

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).

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.

I'm sure Banesh Hoffmann didn't write about bound vectors on
a whim. He was not a lightweight; the Einstein-Infeld-Hoffmann
equation is named after him.  But my hypothesis for today is
that when it comes to bound vectors his book is out-of-date
and/or represents a negligible minority view.

I'm not sure, so I offer it as a hypothesis for discussion.

As a subsidiary hypothesis I suggest that many of the things
that people are tempted to call bound vectors can be more
easily and more correctly expressed as _bivectors_.  I'm pretty
sure Banesh Hoffmann was not up to speed on Clifford Algebra.
  http://www.av8n.com/physics/clifford-intro.htm

Maybe it's just me, but I cannot visualize a bound vector.
Every time I try, I get a bivector instead.  I can easily
visualize bivectors!  Maybe somebody could suggest an example
of something that is a bound vector but not a bivector.
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