Deterministic chaos of the elastic pendulum: a study using GeoGebra
DOI:
https://doi.org/10.23925/2237-9657.2024.v13i2p062-081Keywords:
Elastic pendulum, chaotic systems, GeoGebraAbstract
In this work, Lagrange’s equations of motion for the elastic pendulum were derived. The resulting equations are solved numerically using GeoGebra. From the numerical solutions, an applet was built in GeoGebra that allows studying the behavior of the elastic pendulum through phase spaces, trajectory and the numerical solution. An animation of the system was also built to visualize the movement of the spring pendulum. The applet was used to investigate the dynamics of the elastic pendulum, which presents very interesting dynamics as it is non-integrable. Firstly, the system decoupling limits were analyzed, in these limits the system is non-chaotic. The sensitivity to initial conditions was studied when the spring and the pendulum are in resonance, in which case most of the initial conditions lead to chaotic trajectories.
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