Arc length and reparametrisation
General · Mathematics
Study notes
Q: Reparametrize the circle r(t) = (2cos t, 2sin t) by arc length. |r'| = |(-2sin t, 2cos t)| = 2. s(t) = ∫₀^t2 du = 2t: t = s/2. r(s) = (2cos(s/2), 2sin(s/2)). Check: |dr/ds| = |(-sin(s/2), cos(s/2))| = 1 ✓ (unit speed!). (Arc length: natural parameter!)