PyBullet is a Python library that can be used to help make photorealistic simulations. Though we still want simple plots to see how the dynamics evolve over time, having a photorealistic simulator is very helpful to gain an intuitive understanding of the dynamics and for debugging.

This first step of this task is to take a look at how the inverted pendulum dynamics are defined at this url:
https://github.com/jorgejc2/ISS_Lyapunov_Stable_NN_Controllers/blob/main/neural_lyapunov_training/pendulum.py

After understanding these dynamics, you can try putting them into PyBullet and messing around to see if the model makes sense.

The second step would be a simpler quadrotor case (2D case) and seeing if this works in the simulator as well.
https://github.com/jorgejc2/ISS_Lyapunov_Stable_NN_Controllers/blob/main/neural_lyapunov_training/quadrotor2d.py

The code uses the following resource for writing the dynamics in code:
https://underactuated.mit.edu/acrobot.html#section3