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nadia_g Group Title

can some one give me the concept of arc and curvature( related to calculus 3)

  • 2 years ago
  • 2 years ago

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  1. elica85 Group Title
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    curvature is the rate where the unit vector T turns per unit of length. it is calculated \[k=|dT/ds|\]

    • 2 years ago
  2. elica85 Group Title
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    if you are given a position, you can find T by dividing the derivative of position over the absolute value of it. it can be looked at as velocity over speed\[r'(t)/|r'(t)|\]

    • 2 years ago
  3. elica85 Group Title
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    ds refers to arc length parameter for a curve. if you're given a curve r(t)=x(t)i+y(t)j+z(t)k, \[s(t)= \int\limits_{t _{0}}^{t} (dx/dt)^{2}+(dy/dt)^{2}+(dz/dt)^{2} dt\]

    • 2 years ago
  4. elica85 Group Title
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    now, k can be re written as \[k=|(dT/dt)(dt/ds)|\]

    • 2 years ago
  5. nadia_g Group Title
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    hmm.........ok thanx

    • 2 years ago
  6. nadia_g Group Title
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    elica?

    • 2 years ago
  7. elica85 Group Title
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    the purpose of finding an arc length can be thought of as wanting to know how sharp a curve is turning

    • 2 years ago
  8. elica85 Group Title
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    i just finished this class so my explanation might not be detailed enough since i need to understand more but i shared what i can

    • 2 years ago
  9. nadia_g Group Title
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    in which class u r?

    • 2 years ago
  10. elica85 Group Title
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    calc III just had the finals on monday

    • 2 years ago
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