Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

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



On 09/06/2010 08:46 AM, LaMontagne, Bob wrote:
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."

In particular, that is their definition of "bound vector"
http://www.answers.com/topic/bound-vector

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.

1) Thanks for the pointers.

2) Gaak! I wish I had understood this before replying to Bob S.
a moment ago. His remarks were more on-target than I realized.

I abjectly apologize (again!) and retract what I said. I offer
the following translations instead:

"free vector" --> vector
i.e. honest-to-goodness vector
i.e. direction and magnitude only
"bound vector" --> pair of vectors.

Sometimes the "bound vector" is a pair of vectors of the same type,
which includes the case where it is a pair of position vectors,
in which case the bound vector is almost equivalent to a pair of
points.

In other cases the "bound vector" is a pair of vectors of different
type, such as a point-of-application (which is a position vector)
paired with a force vector, which is something else entirely, living
in a completely different vector space, having different dimensions
(in the dimensional-analysis sense) et cetera.

Bob S. suggested that a "bound vector" under this interpretation is
just a weird way of talking about a vector field, or some element
of a vector field. I need to think about that some more, but at the
moment that sounds right to me.

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

As they should, IMHO.

and then later the term "point of
application" is introduced without rationalization with the previous
definition.

I'm not sure it needs to be connected with the previous definition.

The force-vector and the point-of-application vector are IMHO two
different vectors. They are both important, but they are not the
same thing.

Sleep is important and exercise is important, but we don't define
sleep in terms of exercise or vice vesa.