Help in re-parameterizing the curve

[sarah7]

Hi,

can someone help in re-parameterizing the curve

δ(t)=(2/3(√(L^2+9))cos(t),1/3(√(L^2+9))sin(t),L)

I found dδ/dt then I got the speed to be 1/3√(L^2+9)√(1+3sin^2(t))

L is just a constant z=L

I know how to re-parameterize curves to make them parameterized by arc-length when I get a constant speed but here the speed is in terms of t!

Thanks

 

[hoops]

You should get the integral of ||ds/du|| from zero to t, then you find the function h(t). After this you should find the inverse of h(t), say it is the function f(t), then you find the composition of your original curve and f(t), the new curve is a curve that is parametrized by arc length.