# Discrete Mathematics & Theoretical Computer Science

## Volume 1 n° 1 (1997), pp. 149-157

author: | Alex J. Dragt |
---|---|

title: | A Lie connection between Hamiltonian and Lagrangian optics |

keywords: | Lie algebra, Hamiltonian and Lagrangian optics |

abstract: | 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. |

reference: | Alex J. Dragt (1997),
A Lie connection between Hamiltonian and Lagrangian optics,
Discrete Mathematics and Theoretical Computer Science 1, pp. 149-157 |

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