God’s Own Equation Solved with Python
Your Daily Dose of Scientific Python
If you walk over the campus at Princeton University and visit the university chapel, watch out for the stone engravings above the windows and doors. On one of them, you will find the following equation:
Forget about 𝐸=𝑚𝑐² or whatever popular equation of physics you think is the most important. The one above is the one everyone should really know. In a sense, it could rightfully be called God’s own equation. And that’s probably why it is engraved in the university chapel of Princeton. The official name of the equation is the Euler-Lagrange equation. But why is it so important? Because it is behind each and every established physical theory we have. From classical mechanics to electrodynamics, even general relativity and quantum field theory. All those theories can be expressed in terms of Lagrange functions and Euler-Lagrange equations. Even the sacred energy conservation law can be considered as not fundamental but as an immediate consequence of symmetry properties of 𝐿.
In this post, I will give you a short introduction into the Lagrange formalism and give some simple example with Python code. This shall lay the groundwork for later articles, where the power of the method will become more transparent.
