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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/221967
Cálculo del ángulo entre separatrices en el sistema del péndulo rápidamente forzado
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La medida de las separatrices divididas del péndulo forzado rápidamente
$$
\ddot{x}+\sin x=\mu \sin \left(\frac{t}{\epsilon}\right)
$$
es considerado como un problema que ha sido estudiado por diferentes autores.
En este trabajo, estudiamos el ángulo entre las dos separatrices. Observamos que el ángulo de escisión en este sistema es de órdenes muy bajos y, por ello, para su cálculo nos hemos visto obligados a utilizar aritmética de alta precisión.
Concretamente, para su estudio, hemos creado un programa en C que hace uso de MPFR (aritmética de alta precisión) para analizar cómo varía el ángulo con cambios en los parámetros $\epsilon$ y $\mu$.
The measure of the splitting of the separatrices of the rapidly forced pendulum $$ \ddot{x}+\sin x=\mu \sin \left(\frac{t}{\epsilon}\right) $$ is considered as a model problem that has been studied by different authors. In this work, we study the angle that separates the separatrices. We observe that the splitting angle in this system is of very small orders, and thus, for its calculation, we have been compelled to use high-precision arithmetic. Specifically, for this study, we have created a program in C that uses MPFR (highprecision arithmetic) to analyze how the angle varies with changes in the parameters $\epsilon$ and $\mu$.
The measure of the splitting of the separatrices of the rapidly forced pendulum $$ \ddot{x}+\sin x=\mu \sin \left(\frac{t}{\epsilon}\right) $$ is considered as a model problem that has been studied by different authors. In this work, we study the angle that separates the separatrices. We observe that the splitting angle in this system is of very small orders, and thus, for its calculation, we have been compelled to use high-precision arithmetic. Specifically, for this study, we have created a program in C that uses MPFR (highprecision arithmetic) to analyze how the angle varies with changes in the parameters $\epsilon$ and $\mu$.
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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2025, Director: Àngel Jorba i Monte
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RODRÍGUEZ VIA-DUFRESNE, Ignacio. Cálculo del ángulo entre separatrices en el sistema del péndulo rápidamente forzado. [consulted: 18 of June of 2026]. Available at: https://hdl.handle.net/2445/221967