Abstract
Hamiltonian formalism and the infinite-dimensional modal system describing nonlinear sloshing an imcompressible fluid with irrotational flow partially occupying a tank is derived in general form. The tank has vertical walls near the free surface. The derivation is based on the V.Zhakarov (1967) and W.Craig (1994). The free surface elevation (canonical coordinate) and velocity potential on the free surface (canonical momentum) are expanded in generalized Fourier series. Hamiltonian is expressed in modal coordinates of the free surface elevation and velocity potential on the free surface. The theory is invalid when either the wave angle is large (more than 45 degree). Next, Normal Mode was applied to the obtained canonical equation. As a result, an important mode was clarified.
