European Physical Journal C: Particles and Fields (Jan 2022)

Helmoltz problem for the Riccati equation from an analogous Friedmann equation

  • Valerio Faraoni

DOI
https://doi.org/10.1140/epjc/s10052-021-09966-0
Journal volume & issue
Vol. 82, no. 1
pp. 1 – 6

Abstract

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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–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.