Orthogonality in the hyperbolic plane

• Autores: Domingo Gámez Domingo, Miguel Pasadas Fernández, Rafael Pérez García
• Localización: VIII Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques / coord. por Manuel Pedro Palacios Latasa, David Trujillo, Juan José Torrens Iñigo, Monique Madaune-Tort, María Cruz López de Silanes Busto, Gerardo Sanz Sáiz, 2003, ISBN 84-7733-720-9, págs. 151-159
• Idioma: inglés
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• Resumen

  • Guidelines for an analytical treatment of the small-amplitude orbital motion of a particle of negligible (infinitesimal) mass about the libration points in the planar elliptic restricted three-body problem (ERTBP) are outlined. Keywords: In this paper three essential construction are considered, construction which involve the orthogonality in the models of Poincaré for the hyperbolic plane: a) Determination of the line orthogonal to another one given through a point of it. b) Determination of the unique orthogonal line to a pair of ultraparallel lines. c) Determination of the line orthogonal to another one given through an outer point. This construction apply to the resolution of many problems of the plane hyperbolic geometry.