A Lie connection between Hamiltonian and Lagrangian optics
| Autor: | Alex J. Dragt |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 1997 |
| Předmět: | |
| Zdroj: | Discrete Mathematics & Theoretical Computer Science, Vol 1, Iss 1 (1997) |
| Druh dokumentu: | article |
| ISSN: | 1462-7264 1365-8050 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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