Further transformations may involve c u r v a t u r e = c = 1 R , ω ω = v R = v c and corresponding derivatives: R ˙ ˙ = − − c ˙ ˙ c 2 R ¨ ¨ = 2 ( c ˙ ˙ ) 2 c 3 − − c ¨ ¨ c 2 ω ω ˙ ˙ = v ˙ ˙ R − − R ˙ ˙ v R 2 = v ˙ ˙ c + v c ˙ ˙