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- W2507935901 abstract "Recebido em 17/6/2010; Aceito em 27/12/2010; Publicado em 21/3/2011En este trabajo se muestra que a trav¶es del dominio de la teor¶‡a general de pequenas~ oscilaciones es posibleresolver anal¶‡ticamente los modos vibracionales de la mol¶ecula triangular, y que a la luz de resultados compara-tivos entre la mol¶ecula lineal y triangular se puede evaluar la din¶amica de la mol¶ecula triangular y simpliflcar elan¶alisis. Para ilustrar lo anterior, se modela mec¶anicamente una mol¶ecula triat¶omica, utilizando la formulaci¶onde Lagrange y asumiendo un tipo de mol¶ecula en la cual las masas (¶atomos) est¶an ubicadas en los v¶ertices deun tri¶angulo rect¶angulo. Para un desarrollo anal¶‡tico del problema se utiliza la teor¶‡a de pequenas~ oscilaciones,considerando las masas y las constantes de acoplamiento iguales. Esto ultimo¶ permite escribir el Lagrangianodel sistema en forma adecuada y posteriormente determinar las ecuaciones diferenciales de movimiento, que de-scriben el comportamiento de la mol¶ecula y permiten determinar las frecuencias propias de vibraci¶on. Tambi¶ense analiza y discute el caso de una mol¶ecula triat¶omica lineal, determinando los correspondientes modos normalesde vibraci¶on. Finalmente, se comparan las soluciones de ambos sistemas.Palabras-clave: mol¶ecula triat¶omica triangular y lineal; oscilaciones pequenas;~ modos vibracionales.This work shows that by means of knowledge of the general theory of small oscillations is possible to solveanalytically the vibrational modes of the triangular molecule, and from comparative results between the linearand triangular molecule can access the dynamics of the triangular molecule and simplify the analysis. To illus-trate this, is modeled mechanically a triatomic molecule using the Lagrangian formulation and assuming a typeof molecule in which the masses (atoms) are located at the vertices of a triangle. For an analytical treatment ofthe problem we use the theory of small oscillations, considering equal masses (atoms) and coupling constants.This allows to write the Lagrangian, and then to obtain dynamical equations for determining normal vibrationfrequencies. The case of the linear triatomic molecule is analyzed and discussed, determining the correspondingvibrational normal modes. Finally, the solutions for both cases are compared.Keywords: triangular and linear triatomic molecule, small oscillations; vibrational modes." @default.
- W2507935901 created "2016-09-16" @default.
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- W2507935901 date "2011-01-01" @default.
- W2507935901 modified "2023-09-23" @default.
- W2507935901 title "El estudio y ense~nanza de los modos vibracionales de la molecula triatomica (The study and teaching of the vibrational modes of the triatomic molecule)" @default.
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