Stability of floating barges with trapezoidal and pentagonal sections

The issues of stability of the symmetrical equilibrium position of floating barges in liquid, which have trapezoidal and pentagonal sections, are discussed in the paper. The basic principles of static analysis necessary for studying the stability of floating bodies are given. The exact expression for the potential energy of a floating body is constructed and its quadratic approximation is calculated near the investigated equilibrium state for both problems under consideration. Stability conditions are obtained in terms of dimensionless parameters on the basis of these expressions, and each of the problems under discussion has three such parameters. It is checked that for particular variants of a rectangular pontoon and a triangular boat, the previously known results follow from the found stability conditions in both problems. The found solutions are illustrated as a series of stability regions on the plane of two dimensionless parameters when the value of the third parameter varies. This graphical interpretation allows to establish the main qualitative and quantitative features of the constructed solutions and draw key conclusions. The obtained results are interesting from a theoretical point of view and may be of some practical value.