A generalization of the Helmholtz conditions for the existence of a first-order Lagrangian. (English) Zbl 1105.70010
Summary: The paper deals with a generalization of Helmholtz conditions for the existence of a first-order kinetic potential related to a given set of second-order ordinary differential equations. The extension affects the consideration of such ODE systems which are not self-adjoint due to dissipation. Necessary and sufficient conditions are given for the simultaneous existence of two state functions – a Lagrangian and a dissipation function – both of the first-order such that the given set of second-order ODEs results from the well-known Lagrangian approach.
References:
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