A hybrid system of differential equations describing a rigid body attached to two elastic rods

In this paper, we consider the construction of a mathematical model for a mechanical system, which is a rigid body attached to two Euler-Bernoulli beams. Dynamic equations were obtained using the variational principle of Hamilton-Ostrogradsky. The mathematical model is presented in the form of a hybrid system of differential equations, for which the possibility of using a unified approach to the study of free vibrations, proposed in the study of systems of solids attached to one rod, is discussed.