New analytical formulae and theorems for the wave resistance

Wave resistance is an important characteristic of bodies floating on a free surface or moving under it. A significant number of works pioneered by Lord Kelvin (1887) have been devoted to determination of this characteristic. The problem was studied by such eminent scientists as J. H. Michell, T. H. Havelock, L. N. Sretenskii, N. E. Kochin, M. V. Keldysh, M. A. Lavrentiev, and by many others. The overwhelming majority of investigations were carried out in the framework of the linear wave theory. Successes of the nonlinear theory are much more modest and can be characterized by the almost utter absence of accurate analytical results. A simple exact analytical formula for the wave resistance of a two-dimensional body, which moves in a fluid of finite depth, is presented in this work. Two theorems on the wave resistance are proved.