Proof using frenet equations
(R-Rc).(R-Rc)=a^2 where R=R(s) lies on the surface of a sphere
prove R(s)=Rc-pn -1/t*(dp/ds)b where p = curvature t = torsion n is the unit normal and b is the unit binormal
getting to the proof involves differentiating the original equation and then using the Frenet equations to simplify
Questions? (Rc) and (a) would be considered constants?
if so the
first derivative is 2*(dR/ds.(R-Rc))
sencond derviative is 2*(d^2R/ds^2.(R-Rc)+dR/ds.dR/ds)
third derivative is 2*(d^3R/ds^3.(R-Rc)+3*d^2R/ds^2.dR/ds)
I have tried using the Frenet equations along with R'(s) = v where v is unit tangent and R''(s)=dv/ds
any suggestions on where to go from here?