Discrete Mathematics & Theoretical Computer Science, Vol 1 (1997)

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DMTCS vol 1 no 1 (1997), pp. 149-157

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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