If $ S_1 $is the arc length of the locus of center of curvature of a curve, then show that
$$\dfrac{dS_1}{ds} =\dfrac{ \sqrt{(\kappa^2\tau^2 + \kappa^{'2})}}{\kappa^2} =\sqrt{ (\dfrac{\rho}{\sigma})^2+\rho^{'2}} $$
$\kappa$= curvature ,$\,\rho = $ radius of curvature,$\tau$ = torsion, $\sigma=1/\tau = $ radius of torsion.
k' and rho ' I could not figure out what they represent . This is because question itself does not specify these symbols. Sorry for the inconvenience. You might guess why I this question is giving me tough time. But anyone who can guess these symbols and give anyway to approach this problem would do a huge favour on me.
My approach: My knowledge and resources to study this topic is limited. I know derivative of radius of curvature is derivative of arc length of locus of center of curvature. But can't move beyond this point. Could Somebody throw some light on way forward for this question.
Thanks.