Publication: Introducción a la geometría simpléctica y los sistemas integrables
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2018-06
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El objetivo principal de este trabajo es demostrar el teorema de Arnold-Liouville, que da una condición suficiente para saber si un sistema mecánico hamiltoniano es integrable por cuadraturas. Con este propósito, definimos y desarrollamos los conceptos necesarios para el teorema, dando unas nociones elementales sobre geometría simpléctica y su aplicación a la Mecánica Clásica.
The main goal of this work is to prove the Arnold-Liouville theorem, which gives a sufficient condition for a Hamiltonian mechanical system to be integrable by quadratures. To that end we define and develop the concepts involved in the theorem, giving some elementary notions of symplectic geometry and its application to Classical Mechanics.
The main goal of this work is to prove the Arnold-Liouville theorem, which gives a sufficient condition for a Hamiltonian mechanical system to be integrable by quadratures. To that end we define and develop the concepts involved in the theorem, giving some elementary notions of symplectic geometry and its application to Classical Mechanics.
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