Abstract
To construct a Birkhoffian formulation of nonconservative nonlinear systems under the condition that the Birkhoffian represents the total physical energy is a difficult task. This paper develops a novel approximate Birkhoffian analytical expression for nonconservative nonlinear systems. Based on the method of perturbation, Birkhoffian formulation of nonconservative nonlinear systems is established under the assumption that the Birkhoffian describes the total physical energy of the corresponding conservative systems, and second order approximate autonomous Birkhoffian functions is derived. Four different examples are studied to show applications of the proposed method.
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