Helmoltz problem for the Riccati equation from an analogous Friedmann equation
arXiv:2112.11526 · doi:10.1140/epjc/s10052-021-09966-0
Abstract
We report a solution of the inverse Lagrangian problem for the first order Riccati differential equation by means of an analogy with the Friedmann equation of a suitable Friedmann-Lemaître-Robertson-Walker universe in general relativity. This analogous universe has fine-tuned parameters and is unphysical, but it suggests a Lagrangian and a Hamiltonian for the Riccati equation and for the many physical systems described by it.
arXiv comment6 pages, no figures, to appear in Eur. Phys. J. C
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