Eigenvalues of boundary value problem for a hybrid system of differential equations

In this paper we consider a boundary-value problem for a hybrid system of differential equations. A hybrid system of differential equations is understood as a system of differential equations composed of ordinary differential equations and partial differential equations. In the capacity of the theoretical foundations of our approach to investigation of the boundary-value problem for the hybrid system of differential equations we propose a method of finding eigenvalues for the boundary-value problem. Application of the Hamilton variation principle for constructing the equations of total dynamics for the systems of interconnected rigid bodies attached to the rod by elastic-damping links necessitates consideration of hybrid systems of differential equations.