Biletsky S. Geometrical modeling of multiple reflections of light and thermal rays in elliptic areas

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0406U003634

Thesis Registration Form

0406U003634.pdf

Applicant for

Specialization

  • 05.01.01 - Прикладна геометрія, інженерна графіка

21-09-2006

Specialized Academic Board

Д26.056.06

Essay

The thesis is devoted to the new solution of a problem of geometrical modeling of billiard paths and them caustics in elliptic areas with the purpose of detection characteristic and beforehand prescribed trajectories. To principal outcomes of work it is necessary to refer a method of visualization of paths of mathematical billiards which constituents are new modes: definition of function of the reflection, allowing scientifically to simplify constructions of paths; implementation of phase portraits of elliptic billiards; implementation caustics N-axis reflections of billiard rays; and also laying-out of billiard rays in fields of forces and the combined areas. Algorithmic implementation of following indications is developed: cyclicity of paths which pass through the set point; amounts of initial traffic routes of a point for reaching the set rule under condition of the set amount of reflections; extents of "denseness" filling of an ellipse with paths; paradox at transiting a path through focal points which has allowed to show a phenomenon of unstable stability of computing process obviously.

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