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What equation are these?

  1. Sep 18, 2008 #1
    Does anyone know what equations are these (please see attached image)?

    Also, does anyone know these complete equations?

    Thank you
     

    Attached Files:

  2. jcsd
  3. Sep 18, 2008 #2

    Mech_Engineer

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    They look like they could be related to rotational dynamics, as terms for angular speed ( [tex]\omega[/tex] ) radius ( [tex]r[/tex] ) and time ( [tex]t[/tex] ) are in them. It's also possible they are related to some form of harmonic oscillation, based on the [tex]sin(\omega t)[/tex] terms I see in there.

    However they look like they are probably based a specific geometry, as they don't look generalized to me. Where did you see these equations, and what was the context of their presentation?
     
    Last edited: Sep 18, 2008
  4. Sep 18, 2008 #3

    minger

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    The lambda [tex] \Lambda [/tex] and what Mech_ said makes me think they rotordynamic oriented as well.
     
  5. Sep 18, 2008 #4

    FredGarvin

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    The r/L term is usually a slenderness ratio in shaft dynamics. I'll have to look through my rotor dynamics handbook. I agree with Mech in that I bet this is a derivation for a specific condition/geometry. It definitely is taking me back to the days of harmonic functions and Fourier transforms...
     
  6. Sep 18, 2008 #5

    Mapes

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    I don't disagree with this, but on the far right of the photo it looks like L is the length of a bar connected to a rotating radial link with length r. That would make

    [tex]\sqrt{L^2-r^2\sin^2\omega t}=L\sqrt{1-\left(\frac{r}{L}\sin\omega t\right)^2}[/tex],

    which appears in one of the equations, the y coordinate of the end of the bar.
     
  7. Sep 19, 2008 #6
    How do you know that the equation is dedicated to specific geometry?

    If so, what kind of geometry is it? 2 or 3 dimensional?
     
  8. Sep 19, 2008 #7

    FredGarvin

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    I think you're right on that. I saw the "a" on the circumference of the circle and thought that r may be the radius of the bar with length L. Your slant is more probable. I wonder if it's just a kinematics equation for a linkage, like you mentioned...
     
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