Frenet Serret formulas

Question

The following set of relations (space derivatives) of the fundamental vectors t, n and b are collectively known as the Frenet Serret formulas.

dt/ds = Kn

db/ds = −τn

dn/ds = τb − Kt

How do we apply Frenet Serret formulas for below problem?(since the parameter of vector r is not s, but theta)

Problem: Find t, n, b, K and τ for the curve given by

r = (a cos θ, a sin θ, cθ)

Answer 1

Hi Ashley,

In order to use the Frenet Serret formulas, you should transform the curve into the arc length parameterization. That means you will reparameterize in such a way that the new parameter is the arc length s.

If you are not sure how to do this, I am happy to explain the process.