Consider rrightarrow t were t 0 find the curvature K of th

Consider rrightarrow (t) = were t > 0 find the curvature (K) of the Path given for rrightarrow (t) What\'s the rate of change of K at t = 2 Hint: K = ITrightarrow (t) / IRrightarrow (t)

Solution

r = cost + tsint , sint - tcost T = dr/dt ==-sint +tcost+ sint , cost +tsint -cost ==tcost,tsint K = dT/dt ==-tsint +cost,tcost+sint Hence the radius of curvature = <-tsint +cost,tcost+sint> rate of change of K =dK/dt =-tcost -sint -sint,-tsint+cost +cost =-tcost -2sint,-tsint + 2cost