Caracterização da dinâmica do pêndulo duplo: uma análise numérica e experimental

• Autor(a) principal: Baroni, Rodrigo Simile [UNESP]
• Data de Publicação: 2017
• Tipo de documento: Trabalho de conclusão de curso
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://hdl.handle.net/11449/156910; http://www.athena.biblioteca.unesp.br/exlibris/bd/capelo/2018-08-30/000905728.pdf
• topic: Sistemas dinâmicos diferenciais; Pêndulo; Análise numérica; Sistemas hamiltonianos; Comportamento caótico nos sistemas

In this work we developed a qualitative description of the dynamics of the Double Pendulum, a dynamical system that presents behavior sensitive to the initial conditions. After the analytical treatment, with the objective of analyzing and evidencing both the regular behavior (characterized by periodic and quasi-periodic orbits) and the irregular behavior (characterized by chaotic orbits) exhibited by the system, we studied numerical results, obtained through computational simulations, and experimental results, obtained from the digital treatment of videos of a double pendulum. The Poincaré sections for di erent energy values shows that the system has a mixed phase space, in which regular and irregular orbits coexist, a typical characteristic of Hamiltonian Systems. For low energies there are only regular orbits. The chaotic behavior arises with the increase of energy and was evidenced by the calculation of the Lyapunov exponent from numerical and experimental results