Chaotic electrical circuits analogs for mechanical pendulums

Mechanical pendulums, such as the double pendulum, are classical systems that exhibit deterministic chaotic motion for specific initial conditions. In this work we explore through both simulations and physical implementations analog oscillating electronic circuits that exhibit similar chaotic dependencies. The circuits use operational amplifiers, analog multipliers, and nonlinear components to replicate behaviors observed in equivalent mechanical systems. This type of implementation provides rich opportunities for students to explore chaotic non-linear phenomena in setups that allow for precise control over relevant circuit parameters. This approach also emphasizes the universality of the non-linear phenomena observed across both mechanical and electrical phenomena.