Re: resolve to perpendicular components, because they are independent


kenneth.bull@xxxxxxxxx wrote:
> Hi Physicers,
> Any help will be greatly appreciated.
> It is my understanding that we often resolve vectors (like force,
> velocity) into perpendicular components because they are so called
> "independent." If one component changes value, it doesn't affect the
> value of the other pependicular components (I guess this is where
> "Independent comes from").
> Yet I have been recently shown how to resolve vectors (force) into
> components that aren't perpendicular using a reverse-parallelogram
> rule. Say a force is acting on a structure like < at the left point, I
> have to resolve it into two forces alone the two branches (not
> orthogonal). I encountered this in my self study of certain questions,
> so I don't really have anyone reliable to ask why this is viable in
> light of my previous knowledge of "independent vectors need to be
> perpendicular."
> Can someone shed light on any of this?

I think you want to study the *Kronecker Delta*. I accept that
a number of axes x^1, x^2...x^n are *independant* if
((& is partial))

&x^a / &x^b = 1 if a=b, and 0 if a=/=b.

Is this a structural engineering question?
Ken

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