Helmoltz problem for the Riccati equation from an analogous Friedmann equation
General Relativity and Quantum Cosmology
2022-01-26 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2112.11526,
title = {Helmoltz problem for the Riccati equation from an analogous Friedmann equation},
author = {Valerio Faraoni},
journal= {arXiv preprint arXiv:2112.11526},
year = {2022}
}
Comments
6 pages, no figures, to appear in Eur. Phys. J. C