Regular Article - Theoretical Physics
Helmoltz problem for the Riccati equation from an analogous Friedmann equation
Department of Physics and Astronomy, Bishop’s University, 2600 College Street, J1M 1Z7, Sherbrooke, QC, Canada
Accepted: 21 December 2021
Published online: 7 January 2022
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.
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