# Tangent, Normal, Binormal, Curvature, Torsion

1. Sep 20, 2006

### Mindscrape

Okay, so I was asked to find all the things listed in the topic title given the equation:
$$r(t)=(cos^{3}t)\vec{i} + (sin^{3}t)\vec{j}$$

Now this is a lot of work, especially when it comes to finding the torsion $$\tau = - \frac{d \vec{B}}{ds} \cdot \vec{N}$$ a total of four derivitives. Maybe I am missing something about how these all relate, and I could somehow get around all the work. I would put up my work so far, but that would take a really long time.

Basically, what I have done is find the tangent vector, so v/mag(v); the normal vector, derivative(tangent)/mag(tangent); the binormal, TxN; and now I got to Torsion (d(binormal)/dt)/mag(v) dot N. Torsion looks like it will be a long equation with my method.

Thoughts?

Last edited: Sep 20, 2006