Centers of inscribed circles in triangular orbits of an elliptic billiard
Ronaldo A. Garcia
TL;DR
This paper investigates the geometric locus of inscribed circle centers in 3-periodic elliptical billiard orbits, revealing it forms an ellipse and deriving its canonical equation, extending prior research.
Contribution
It provides the explicit canonical equation of the ellipse formed by the centers of inscribed circles in triangular billiard orbits, advancing understanding of elliptical billiard dynamics.
Findings
The locus of inscribed circle centers is an ellipse.
The canonical equation of this ellipse is derived.
This work extends previous results by O. Romaskevich.
Abstract
The locus of centers of inscribed circles in triangles, the 3-periodic orbits of an elliptic billiard, is also an ellipse. In this work we obtain the canonical equation of this ellipse, complementing the previous results obtained by O. Romaskevich.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Advanced Differential Equations and Dynamical Systems