Geodesic
Elliptic billiard with cosine law of refraction on confocal quadrics
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2025), pp. 16-23

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For a billiard in an elliptic domain, we consider several confocal quadrics, which divide this domain into several regions each filled with homogeneous media with various densities. When crossing the quadric separating two media, it is assumed that the trajectory deviates from a straight line according to the modified (cosine) law of refraction. For the system obtained in this way, the constant of motion is obtained. 
@article{VMUMM_2025_2_a2,
     author = {M. A. Nikulin},
     title = {Elliptic billiard with cosine law of refraction on confocal quadrics},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {16--23},
     publisher = {mathdoc},
     number = {2},
     year = {2025},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2025_2_a2/}
}
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M. A. Nikulin. Elliptic billiard with cosine law of refraction on confocal quadrics. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2025), pp. 16-23. http://geodesic.mathdoc.fr/item/VMUMM_2025_2_a2/