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arXiv · 1702.08566

Superintegrable classical Zernike system

George S. Pogosyan·Kurt Bernardo Wolf·Alexander Yakhno
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Abstract

We consider the differential equation that Zernike proposed to classify aberrations of wavefronts in a circular pupil, as if it were a classical Hamiltonian with a non-standard potential. The trajectories turn out to be closed ellipses. We show that this is due to the existence of higher-order invariants that close into a cubic Higgs algebra. The Zernike classical system thus belongs to the class of superintegrable systems. Its Hamilton-Jacobi action separates in three vertical projections of polar coordinates of a sphere, polar and equidistant coordinates on half-hyperboloids, and also in elliptic coordinates on the sphere.

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George S. Pogosyan, Kurt Bernardo Wolf, Alexander Yakhno. 2017-02-27. Superintegrable classical Zernike system. https://doi.org/10.1063/1.4990793

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