Equivalence to dissipative Hamiltonian realization

This paper considers the problem of deriving a generalized Hamiltonian potential for autonomous dynamical systems. For a given vector field, the objective is to construct a locally defined dissipative Hamiltonian generating function for the system. The proposed approach consists of studying the deviation of the given vector field from a canonically defined Hamiltonian vector field. First, we obtain a one-form by taking the interior product of a nonvanishing two-form with respect to the vector field. We then construct a homotopy operator on a star-shaped region that decomposes the system into an exact part and an anti-exact one. Equivalence between the exact part and an exact one-form generated from a known potential is then used to compute the locally defined dissipative potential of the original system. An example is presented to illustrate the method.