Theoretical Foundations of the Study of a Certain Class of Hybrid Systems of Differential Equations

In this paper, we consider boundary-value problems for a new class of hybrid systems differential equations whose coefficients contain the Dirac delta-function. Hybrid are that both ordinary and partial equations; such appear, example, when motion mechanical rigid bodies attached to beam by elastic bonds derived from Hamilton–Ostrogradsky variational principle. We present examples lead introduce notions generalized solutions eigenvalues problem. also compare results numerical simulations based on methods proposed in paper with obtained previously known show our approach is reliable universal.