Lurie equations and equivalent Hamiltonian systems

—This paper proposes new approachesto constructing equivalent Hamiltonian systems for linear and nonlinear Lurie equations (differential equations containing the derivatives of even orders only). The approaches are based on the transition from the linear part of the Lurie equation to the normal forms of the corresponding Hamiltonian systems, with a subsequent transformation of the resulting system. This scheme does not require complex and cumbersome transformations of the original equation. The effectiveness of the formulas derived is illustrated by examples.