Thanks for your response, I could have included more information in my original reply.

You are correct that Harlan and I do include more complex topics in our articles. However, we aim to do so in a way where someone with a general science background could follow our reasoning and learn about the concept we are teaching. To be completely honest, I do not think your article accomplishes this goal. It reads more like a textbook derivation or an excerpt from a Wikipedia article. The fact that you are planning this to be a series is probably contributing to this writing style. I know that Lagrangian mechanics are very cool and interesting from my time taking classical mechanics, however, the wow factor just doesn't come across here.

I think you have a start for what potentially could be a really cool article. My advice would be to focus on the example you provide at the end. Include some more visuals of the particle in motion. You could even solve the same problem with Newtonian and Lagrangian methods to contrast how efficient the Lagrangian method is. The discussion about the potential trajectories an object can take is very interesting, more of that stuff would be great. Additionally, I think streamlining a lot of your explanation would make this a lot more interesting. You want to think of it like taking your readers along for the ride of your thought process. Why should we care about this topic?

If you want to maintain your current style, go for it. There is definitely an audience for that on Medium, it's just not really what we want to publish on Science Spectrum.