(1)

and transverse velocity

u sin θ − v cos θ = ( l − c1) u sin θ ≈ (β − α) u sin θ;
c2

(2)

and the time of completing a turn of the spiral is 2π/μ.

When μ has the critical value in (7),

= C2cos θ = (x2 + 1) cos θ,
μ pC1 p

(3)

which makes the circumference of the cylinder on which the helix is wrapped

(u sin θ − v cos θ = 2πu(β − α) (x2 + 1) sin2 θ cos θ
μ p