The Routhian is intermediate between L and H ; some coordinates q 1, q 2,..., q n are chosen to have corresponding generalized momenta p 1, p 2,..., p n, the rest of the coordinates ζ 1, ζ 2,..., ζ s to have generalized velocities dζ 1 / dt, dζ 2 / dt,..., dζ s / dt, and time may appear explicitly;