Equivalent Hamiltonian Systems for Differential Equations with Even Order Derivatives

New approaches are proposed in the problem of constructing equivalent Hamiltonian systems for linear Lur’e equations (differential equations containing derivatives of even orders only). The approaches are based on the transition to the normal forms of the corresponding Hamiltonian systems with subsequent transformation of the resulting system. The proposed scheme does not require complex and cumbersome transformations of the original equation. It is shown that this problem is uniquely solvable. The appendix provides similar results for systems with two degrees of freedom. The effectiveness of the proposed formulas is illustrated by examples.