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udvat

Finding length of a curve

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given du/dt= a(-3+6t-3t^2) + b(9t^2-12t+3) + c(-9t^2+6t) + 3t^2d dv/dt= a1(-3+6t-3t^2) + b1(9t^2-12t+3) + c1(-9t^2+6t) + 3t^2d1 dw/dt= a2(-3+6t-3t^2) + b2(9t^2-12t+3) + c2(-9t^2+6t) + 3t^2d2 f(t) =sqrt [ (du/dt)^2 + (dv/dt)^2 + (dw/dt)^2]............................(1) L=integration of f(t) in the range [tmin,tmax]..................................(2) Question 1: is it possible to find f(t)? plz help Question 2: if I dont do the sqrt as (1) I get f(t)*f(t)= (du/dt)^2 + (dv/dt)^2 + (dw/dt)^2....................(3) then I can integrate (3) and get L'' L''=integration of f(t)*f(t) in the range [tmin,tmax] how can I get L from L''?

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So, let's think about this from a different perspective.

Say you have a velocity vector. If you're given only Vx, Vy, and Vz, how do you find V?

Well, V = sqrt(Vx^2 + Vy^2 + Vz^2) right?

Velocity is, however, just the time-derivate of the position R. Therefore:

dR/dt = sqrt((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2)

Which looks familiar. Only in your case, you have "V" but you want "R". How do you find R?
Can you use R = sqrt(x^2 + y+2 + z^2)?

Do you see a way to get u,v, and w?

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1. At first glance, looks very messy. I would likely use a numerical approximation.

2. No.

(Note: I plugged the given problem into Maple, and after 800 seconds it is still working on the solution which is sort of reassuring that my first glance was correct.)

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Quote:
Original post by udvat
NO. I dont want to get u,v,w. I want to get the length L.


Ok, let me be more direct. This looks like schoolwork, so I'm hesitant to just give you the answer. I realize that you want L, and I'm asserting that you can find L by working with u,v, and w. My previous post was an analog of your particular problem. Try assuming that I wrote it because it's relevant and not because I'm too confused to understand a simple question.

Because it looks like schoolwork, it's still up to you to figure out why it's relevant. If you do, then finding L will become trivial.

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Thanks Mastaba,yes, I applied numerical approximation and it is working.

And Errision,for your kind information,it is not any school assignment.
I dont understand why do you hesitate to help someone to figure out a solution thinking that its a school task? There is no crime in helping in a school assignment too.(I think)
Because you are just showing the way, you are not solving the whole problem.

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Quote:
Original post by udvat

Thanks Mastaba,yes, I applied numerical approximation and it is working.

And Errision,for your kind information,it is not any school assignment.
I dont understand why do you hesitate to help someone to figure out a solution thinking that its a school task? There is no crime in helping in a school assignment too.(I think)
Because you are just showing the way, you are not solving the whole problem.


It's the rules here :)

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