Equation of a Curve in R3 with Constant Inclination: Need Help!

[ziggy]

I'm trying to find the equation of a curve in R3 where k=t=a/(s^2+b) where k is the curvature, t is the torsion and a,b are constants contained in R. I've spent weeks on this problem and at the moment it's driving me nuts since I always seem to end up with an impossible integral. Any help or hints would be much appreciated. Thanks.

 

[Reb]

This is called a curve of 'constant inclination', as t/k=1=cotan(a),
where a is a constant angle formed
by the tangent to the curve and a specific fixed direction. This will make integration easier.


Ps. There is (free) software on the internet, which will draw a curve on the input of its k and t.