1. Install python 3.6 or later (needs format strings and type hinting)
2. Set up a virtualenv: virtualenv .venv and source .venv/Scripts/activate
3. Install dependencies pip install -r requirements.txt
4. Run what you want (see below).

There are multiple files to run.
You can run a jupyter notebook for some graphs and lots of sample code: jupyter notebook then open Test data.ipynb.
Or run one of the three main files with python: find_best_braking_factor.py, plot_numerical_model.py, obstacle_height_tester.py.

A rendered version of Test data.ipynb can be found in Test data.html, so you don't need to run jupyter to see the results.

The braking factor is a coefficient used in acceleration to simulate drag and other sources of energy loss.
The ball is rolling, not sliding.
The track is represented with a parabola.
The goal was to elevate the center of the parabola to a certain height, where the ball could pass exactly twice.

Calculated values and a simulation:

A gif of a rolling ball, with no obstacle:

A gif with an obstacle: