Stability of floating bodies with movable load

The paper considers two problems on the floating stability of rectangular and triangular bodies, on which a semicircular bar is symmetrically placed in the initial equilibrium position. The main principles of stability research by analytical statics methods are presented, and the necessary expression for the potential energy of a floating body with an additional solid load in general form is constructed. For these problems, the most interesting version of a movable semicircular bar relative to the floating body is considered, and the version when they are rigidly connected to each other is discussed. The obtained stability conditions, taking into account the introduction of dimensionless parameters in each of the designated options for both problems, are compared with each other, as a result of which similarities and differences in their formula notation are revealed. These conditions, together with the feasibility condition, are displayed in a visual graphical form as families of boundaries of stability regions on the plane of two dimensionless parameters for different values of the third parameter. The results found are of fundamental importance for analytical mechanics and stability theory and they can find some application in practice.