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- Introduction
- The project
- Non-linear dynamics
The project
The pendulum we are studying here will be able, under certain conditions, to display a chaotic [ref] behaviour.
This pendulum is constituted by a mass suspended with a string of neglectable weight, hanging on a bracket which weight is also neglectable, and itself lying on a rotative disc. We will be interested in the case where we bend this system by an angle $\alpha$ with respect to the gravity's acceleration.
Our project will consist of this system's study : we will begin by studying similar but simpler systems, and then increase the difficulty gradually to finally reach the case of the chaotic pendulum. From then on we will be able to characterise the pendulum's trajectory, study its chaotic behaviour, and search its fixpoints, whether stable or not.