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Nonimaging Optics by With contributions by Narkis Shatz and John C. Bortz, Pablo G. Benitez, Juan C. Minano, Roland Winston

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Appendix C CONSERVATION OF SKEW AND LINEAR MOMENTUM

C.1 SKEW INVARIANT

The conservation of skew in rotational symmetric systems or the conservation of linear momentum in the linear symmetric ones comes easily in the Hamiltonian formulation. The Hamiltonian system is given by Eq. (6.16) for a system i1, i2, i3 of orthogonal coordinates. For a rotationally symmetric system, let us assume that θ is the coordinate of the symmetry—that is, ∂n/∂θ = 0, where n is the refractive index distribution function. We will identify θ with i2 of Eq. (6.16). Then we have

image     (C.1)

where the Hamiltonian function is

     (C.2)

a1, a2, and a3 are, respectively, ...

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