Variational principles associated with ship motions in waves

General variational principles for linear water waves are obtained. Reasonable algorithms to calculate hydrodynamic quantities, which are important in discussing ship motions in waves, are obtained from the standpoint of the variational principles. A general form of the equation of ship motions in ocean waves is discussed. A general theory of one-dimensional tidal waves is also discussed, and the corresponding variational principle is obtained. Using this principle, a simple numerical example is given to show the character and importance of the variational principle.