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The Jacobi metric derived from the line element by one of the authors is shown to reduce to the standard formulation in the non-relativistic approximation.
L.P. Eisenhart, Dynamical Trajectories and Geodesics
1928
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E. Zermelo, ’́Uber das Navigationsproblem bei ruhender oder ver’́anderlicher Windverteilung
1931
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G. Randers, On an asymmetrical metric in the four-space of general relativity
1941
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O.C. Pin, Curvature and mechanics
1975
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C. Duval, G. Burdet, H. P. Künzle, and M. Perrin, Bargmann structures and Newton-Cartan theory
1985
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V.G. Gurzadyan and G.K. Savvidy, Collective relaxation of stellar systems
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V. Perlick, Bertrand spacetimes
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Iwai T., Katayama N., On Extended Taub-NUT metrics
1993
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A.V. Tsiganov, The Maupertuis Principle and Canonical Transformations of the Extended Phase Space
2001
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C. Robles, Geodesics in Randers spaces of constant curvature
2007
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S. Nair, S. Ober-Blöbaum and J.E. Marsden. The Jacobi-Maupertuis Principle in Variational Integrators
2009
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2009
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M. Cariglia, Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
G.W. Gibbons, The Jacobi-metric for timelike geodesics in static spacetimes
2015
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D. C. Brody, G. W .Gibbons D. M. Meier, Time-optimal navigation through quantum wind
2015
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2015
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M. Cariglia, Null lifts and projective dynamics
2015
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D. C. Brody, G. W .Gibbons D. M. Meier, A Riemannian approach to Randers geodesics
2016
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2012
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2014
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B. Rink, Lecture notes on “Geometric Mechanics and Dynamics”
Cited in the paper.
A.A. Izquierdo, M.A.G. Leon, J.M. Guilarte, and M. T. Mayado, Jacobi Metric and Morse Theory of Dynamical Systems
Cited in the paper.
P.L. Maupertuis, (1744), Accord de différentes loix de la nature qui avoient jusqu’ici paru incompatibles , Académie Internationale d’Histoire des Sciences, Paris
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T. Houri, Liouville integrability of Hamiltonian systems and spacetime symmetry
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Grandati Y., Bérard A. and Mohrbach H., Bohlin-Arnold-Vassiliev’s Duality and Conserved Quantities
Cited in the paper.
2016
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