Geodesic
A Lie connection between Hamiltonian and Lagrangian optics
Discrete mathematics & theoretical computer science, Tome 1 (1997).

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It is shown that there is a non-Hamiltonian vector field that provides a Lie algebraic connection between Hamiltonian and Lagrangian optics. With the aid of this connection, geometrical optics can be formulated in such a way that all aberrations are attributed to ray transformations occurring only at lens surfaces. That is, in this formulation there are no aberrations arising from simple transit in a uniform medium. The price to be paid for this formulation is that the Lie algebra of Hamiltonian vector fields must be enlarged to include certain non-Hamiltonian vector fields. It is shown that three such vector fields are required at the level of third-order aberrations, and sufficient machinery is developed to generalize these results to higher order. 
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     author = {Dragt, Alex J.},
     title = {A {Lie} connection between {Hamiltonian} and {Lagrangian} optics},
     journal = {Discrete mathematics & theoretical computer science},
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     year = {1997},
     doi = {10.46298/dmtcs.238},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.238/}
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Dragt, Alex J. A Lie connection between Hamiltonian and Lagrangian optics. Discrete mathematics & theoretical computer science, Tome 1 (1997). doi : 10.46298/dmtcs.238. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.238/

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