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The general results presented above for Hamilton's principle can be applied to optics using the Lagrangian defined in Fermat's principle.The Euler-Lagrange equations with parameter σ =x 3 and N=2 applied to Fermat's principle result in ˙ = with k = 1, 2 and where L is the optical Lagrangian and ˙ = /.
Hamilton's principle states that the true evolution q(t) of a system described by N generalized coordinates q = (q 1, q 2, ..., q N) between two specified states q 1 = q(t 1) and q 2 = q(t 2) at two specified times t 1 and t 2 is a stationary point (a point where the variation is zero) of the action functional [] = ((), ˙ (),) where (, ˙,) is the Lagrangian function for the system.
Optics Letters is a biweekly peer-reviewed scientific journal published by Optica (formerly known as Optical Society of America). It was established in July 1977. The editor-in-chief is Miguel Alonso (University of Rochester). [1] The journal covers all topics pertaining to optics and photonics. Publishing formats are short and rapid ...
Hamilton's principle is still valid even if the coordinates L is expressed in are not independent, here r k, but the constraints are still assumed to be holonomic. [37] As always the end points are fixed δr k (t 1) = δr k (t 2) = 0 for all k. What cannot be done is to simply equate the coefficients of δr k to zero because the δr k are not ...
The Journal of Optics is a peer-reviewed scientific journal covering all aspects of modern and classical optics, experimental and theoretical studies, applications and instrumentation. It is the official journal of the European Optical Society and is published by IOP Publishing .
Journal of Nonlinear Optical Physics & Materials; Journal of Optical Communications and Networking; Journal of Optical Microsystems; Journal of Optics (IOP Publishing journal) Journal of Photonics for Energy; Journal of Physics: Photonics; Journal of the European Optical Society: Rapid Publications; Journal of the Optical Society of America
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Journal of the Optical Society of America, 1917–1983, [16] which was split into two journals in 1984: Journal of the Optical Society of America A, ISSN 1084-7529 (print); ISSN 1520-8532 (online); 1984–present — Covering research on optics, image science, and vision. Journal of the Optical Society of America B, ISSN 0740-3224 (print); ISSN ...