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Need help with this Spiral problem

  1. Dec 5, 2004 #1
    There is a spiral but it is just on the yz plane (no length to it) I need to integrate it. And I'm at a location x on the axis if it matters.

    Thanks
     
  2. jcsd
  3. Dec 5, 2004 #2
    What do you want to calculate? its lenght? if so, let [itex]M(t)[/itex] be your curve, as long as [itex]M'(t) \ne 0[/itex] then

    [tex]Length[M]=\int_{t_0}^{t_1} \sqrt{\dot{x}^2+\dot{y}^2+\dot{z}^2}ds[/tex]
     
  4. Dec 5, 2004 #3
    alpha; which is the angle subtended by a radius at the point of observation (x).
     
  5. Dec 5, 2004 #4

    HallsofIvy

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    I'm sorry but I can't make heads or tails of this.

    "There is a spiral but it is just on the yz plane (no length to it) I need to integrate it."
    ?? You can't integrate a spiral, you can only integrate a function.

    "alpha; which is the angle subtended by a radius at the point of observation (x)."

    What about alpha? A single line does not "subtend" an angle. And what is the "point of observation"?
     
  6. Dec 5, 2004 #5
    What does "subtend " mean ? Can't you mathematicians puy it in words ordinary people can understand . Also "leght " is spelled "length". The expression is "head or tail "for a single event not "heads and tails ". You mathematicians are so precise in everything except the laguage used to express your ideas .
     
  7. Dec 5, 2004 #6
    Sorry "put" not puy (slip of the finger )
     
  8. Dec 5, 2004 #7
    The spiral has a center in the yzx axis (it is like a coil but flat so the radius gets bigger) You can do this by polar coordinates (I was told), but I do not know how. I need to find a vector field that is directed along the x axis. And alpha is the angle subtended by a radius at the point on x.
     
  9. Dec 5, 2004 #8

    He used "subtend" perfectlly...if it were a helix, but its a spiral, so there is no angle. The rest of your complaint is about typos and dialects, which is pointless to get mad about.

    starbaj12, I think you'll need to be more specific in your request for help.

    -Burg
     
  10. Dec 6, 2004 #9
    Line integrals of three space

    You can find it by parameterizing the curve. Spirals are pretty easy to parameterize and would be similar to: x=cos(t) y=sin(t) z=t. Then you can take the integral from start to finish of f(x(t),y(t))|ds|dt. You can find this by looking in the index of any calculus book under line integrals in 3-space or something similar. This isn't usually done until Calculus III, so it would be towards the back of the book.
     
  11. Dec 6, 2004 #10
    also, as halls of ivy just said, you cant go integrating blindly, you need to do it by pieces (where the lenght is well defined, [itex]M'(t)\ne 0[/itex])
     
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