The whorls are flat, subimbricating, and longitudinally costate. The outer surface is smooth, costate or granular. Early genera were almost circular to elongate-oval, with smooth or finely costate shells. In control theory this is formulated instead as costate equations. The five whorls are sloping above, convex, longitudinally irregularly striate, and spirally costate. The sculpture of the shell is often carinate or costate. A costate estimation procedure for the Legendre pseudospectral method was also developed. The costate equation is related to the state equation used in optimal control.