Pêndulos assimétricos acoplados a um suporte móvel livre

Abstract

The main objective of the present work is to obtain, computationally, the analytical expressions resulting from the modeling of a non-linear dynamic system formed by two pendulums, coupled to a mobile support that can move freely on a plane. We consider a situation in which the pendulums have different masses and lengths, that is, asymmetrical, this ends up making the process of obtaining the necessary equations for the study of this system difficult. Thus, we will use the SymPy module (Python for symbolic computation) to assist in the process of deducing the analytical expressions of the modeling of the proposed problem. Then, we will study the phenomenon of energy transfer that can occur between the normal modes of oscillation of the system, trying to determine their stability and the situations in which energy transfer can occur. From the methodological point of view, the research is the result of bibliographic reviews based on theoretical studies of physics and mathematics. It is also worth mentioning that the results observed during the study were obtained from numerical simulations using the Python programming language and specialized modules, such as NumPy and SymPy.