v = dR/dt = dR/ds * ds/dt = T * ds/dt
a = dv/dt = dT/dt * ds/dt + T * =
= dT/dt * (ds/dt)^2 + T *
dT/ds = K*N, where K is the radius of curvature.
a = K(ds/dt)^2 * N + * T
a = aN * N + aT * T
aN = K*(ds/dt)^2 = K |v|^2 = (|v|^2)/rho, where rho is the radius.
aT = = d|v|/dt
aN from above is the centripetal acceleration.