Thread: Find Curvature Question

Find the curvature κ(t) of the parabola x(t) = (t, t^2) for -∞ < t<∞

I've found d2x/dt2 to be 2 and dx/dt to be 2t

using κ(t) = d2dt2/(1 + (dx/dt)^2)^3/2
is there any way I can easily simplify this?

Originally Posted by Playthious

is there any way I can easily simplify this?

No, there isn't.

Regards.

Fernando Revilla

Originally Posted by Playthious

Find the curvature κ(t) of the parabola x(t) = (t, t^2) for -∞ < t<∞

I've found d2x/dt2 to be 2 and dx/dt to be 2t

using κ(t) = d2dt2/(1 + (dx/dt)^2)^3/2

I assume you mean (d2x/dt2)/(1+ (dx/dt)^2)^2/3 in your notation.

is there any way I can easily simplify this?

Well, you could put in the values you got for the first and second derivatives!