Helmoltz problem for the Riccati equation from an analogous Friedmann equation

Author:

Faraoni ValerioORCID

Abstract

AbstractWe 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.

Funder

Natural Sciences and Engineering Research Council of Canada

Publisher

Springer Science and Business Media LLC

Subject

Physics and Astronomy (miscellaneous),Engineering (miscellaneous)

Reference38 articles.

1. H. von Helmholtz, Ueber die physikalische Bedeutung des Princips der kleinsten Wirkung. J. Reine Angewandte Math. 100, 18 (1887)

2. J. Douglas, Solution of the inverse problem of the calculus of variations. Trans. Am. Math. Soc. 50, 71–128 (1941)

3. W. Sarlet, The Helmholtz conditions revisited. A new approach to the inverse problem of Lagrangian dynamics. J. Phys. A: Math. Gen. 15, 1503–1517 (1982)

4. G.E. Prince, D. King, “The inverse problem in the calculus of variations: nonexistence of Lagrangians”, in Differential Geometric Methods on Mechanics and Field Theory: Volume in Honour of Willy Sarlet, F. Cantrijn and B. Langerock editors (Academia Press, Gent, Belgium, 2007), pp. 131–140

5. D.V. Zenkov (ed.), The inverse problem of the calculus of variations: local and global theory (Atlantis Press, Paris, 2015)

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