A helix is defined as,
x(s)=a(s), y(s)=-R(s) cos(2*pi*np*s/l), z(s)=R(s) sin(2*pi*np*s/l) where 0.le.R(s).le.Rh and is given by,
R(s)=Rh[1/pi *arctan(beta*(s/l -gama))+0.5] where beta and gama are constants and np is the no.of turns on the helix. Find
the expression for a(s) such that the tangent vector [x'(s),y'(s),z'(s)] has unit length




Where the amplitude satisfies and is given by,

Where and are constants and is the no. of turns in a helix.

Find the expression for such that the tangent vector has unit length.

Are you sure that x(s) = a(s) and not a*s? In general, the length L is the integral over the parameter s of this function: sqrt (x'(s)^2 + y'(s)^2 + z'(s)^2).

It just means x(s) is a function of s. I used the above formula u mentioned and I tried. But the final integration becoming complex since here R(s) is a function of (s). Can u help me in that... Thanks for your comment

Are you sure you need to calculate the helix length? There is no mention of helix length here. What is asked here is to find a(s) such that [x'(s),y'(s),z'(s)] is a unity vector. You said your integration was complex; what a(s) did you use for integration? Read you original post -- it hasn't come completely through. The last sentences are with gaps and meaningless.

If you select a(s) such that [x'(s),y'(s),z'(s)] has unit length everywhere then sqrt( (dx/ds)^2 + (dy/ds)^2 + (dz/ds)^2 ) = 1 irrespective of parameter s. Then your integration becomes trivial.