Question

"Frenet-serre reference frame"

Answer 1

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).

Answer 2

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

Answer 3

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?

Answer 4

@ganeshie8 @dan815

Answer 5

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

Answer 6

Alright thanks.

Answer 7

GOOD LUCK LOL

Answer 8

Thanks xD

Answer 9

@Empty

Answer 10

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