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arXiv · 2112.11526

Helmoltz problem for the Riccati equation from an analogous Friedmann equation

Valerio Faraoni
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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-Lema\^itre-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.

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Valerio Faraoni. 2021-12-21. Helmoltz problem for the Riccati equation from an analogous Friedmann equation. https://doi.org/10.1140/epjc%2Fs10052-021-09966-0

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