Solutions of the Laplace Equation Satisfying the Condition of Impermeability on a Spherical Segment

Resumo

We construct a set of harmonic functions satisfying the condition of impermeability on a spherical segment. These functions can be used as a functional basis for the construction of approximate solutions of the boundary-value problems of liquid sloshing. The indicated harmonic functions are obtained as a result of the Kelvin inversion of the auxiliary functions satisfying the corresponding boundary condition on an interval of the horizontal line. The constructed system of functions is applied to the determination of natural sloshing frequencies in a spherical tank.