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Zale101

  • one year ago

"Frenet-serre reference frame"

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  1. Zale101
    • one year ago
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    Find T(t), N(t), B(t) at the given point. \(r(t)=(t^2-1)i+tj;~ t=1\) \(r'(t)=2t+1j\) \(||r'(t))||=\sqrt{(2t)^2+1}=\sqrt{4t^2+1}\) \(T(t)=\LARGE \frac{r'(t)}{||r'(t)||}\) \(T(t)=\LARGE \frac{2ti+j}{\sqrt{4t^2+1}}\) \(T(1)=\LARGE \frac{2}{\sqrt{5}}i+\frac{1}{\sqrt{5}}j\) I am having trouble finding N(t).

  2. Zale101
    • one year ago
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    \(N(t)=\large\frac{T'(t)}{||T'(t)||}\)

  3. Zale101
    • one year ago
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    I tried solving for N(t) but when i took the derivative of T(t), it seemed complex in the N(t) equation. Is that okay?

  4. Zale101
    • one year ago
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    @ganeshie8 @dan815

  5. ganeshie8
    • one year ago
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    I think so, there is no easy way... you will have to work the messy derivatives...

  6. Zale101
    • one year ago
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    Alright thanks.

  7. hwyl
    • one year ago
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    GOOD LUCK LOL

  8. Zale101
    • one year ago
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    Thanks xD

  9. ganeshie8
    • one year ago
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    @Empty

  10. Zale101
    • one year ago
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    \(T'(t)=\large \frac{2}{(4t^2+1)^{3/2}}-\frac{4t}{4t^2+1)^{3/2}}\) \(||T'(t)||=\sqrt{\frac{4}{(4t^2+1)^3}-\frac{1}{4t^2+1}^{3/2}}}\)

  11. Zale101
    • one year ago
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    |dw:1443977000437:dw|

  12. Zale101
    • one year ago
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    |dw:1443979370730:dw|

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