## Zale101 one year ago "Frenet-serre reference frame"

1. Zale101

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

$$N(t)=\large\frac{T'(t)}{||T'(t)||}$$

3. Zale101

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

@ganeshie8 @dan815

5. ganeshie8

I think so, there is no easy way... you will have to work the messy derivatives...

6. Zale101

Alright thanks.

7. hwyl

GOOD LUCK LOL

8. Zale101

Thanks xD

9. ganeshie8

@Empty

10. Zale101

$$T'(t)=\large \frac{2}{(4t^2+1)^{3/2}}-\frac{4t}{4t^2+1)^{3/2}}$$ $$||T'(t)||=\sqrt{\frac{4}{(4t^2+1)^3}-\frac{1}{4t^2+1}^{3/2}}}$$

11. Zale101

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12. Zale101

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