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Billard in Ellipsen und Geodäten an Ellipsoiden

In: Ein Schaubild der Mathematik

Author

Listed:
  • Dmitry Fuchs

    (University of California Davis, Dept. Mathematics)

  • Serge Tabachnikov

    (Pennsylvania State University, Dept. Mathematics)

Abstract

Zusammenfassung Das Billardsystem beschreibt die Bewegung eines freien Punktes innerhalb eines ebenen Gebietes: Der Punkt bewegt sich mit konstanter Geschwindigkeit entlang einer Geraden, bis er auf den Rand trifft. Dort wird er entsprechend dem bekannten Gesetz der geometrischen Optik „Der Einfallswinkel ist gleich dem Reflexionswinkel“ gespiegelt. Genauso gut kann man sich Lichtstrahlen vorstellen, die von einem Rand reflektiert werden, der ein perfekter Spiegel ist. Wir werden Billardtische betrachten, die von glatten, konvexen, geschlossenen Kurven γ begrenzt sind. geometrische Optik

Suggested Citation

  • Dmitry Fuchs & Serge Tabachnikov, 2011. "Billard in Ellipsen und Geodäten an Ellipsoiden," Springer Books, in: Ein Schaubild der Mathematik, chapter 0, pages 437-457, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-12960-5_28
    DOI: 10.1007/978-3-642-12960-5_28
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