eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
1997-01-01
Vol. 1
10.46298/dmtcs.238
238
journal article
A Lie connection between Hamiltonian and Lagrangian optics
Alex J. Dragt
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.
https://dmtcs.episciences.org/238/pdf
Hamiltonian and Lagrangian optics
Lie algebra
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]