Summer of Math Exposition

You made it very clear, how we come from one conclusion to the next. However, the proof of the minimazation formula of \int_{t_a}^{t_b}K(\dot x)-U(x)dt is a bit lenghy and wordy and may have been worth leaving out since it hooked off the main idea of the video.

nice visual representation but sadly the audio was a little fried

Making graphics for this video looks like it was a lot of fun. It is very equation based and would take a long time to digest, which makes it more of a university lecture-style presentation where the intended audience for this video is more people who understand many of the concepts already and this just explores different ways of using the concepts.

I really like what you had going on with the steamroller example, that’s a very nice way to introduce the notion of the calculus of variations to anybody who isn’t familiar with it. That said, I think the transition from that to the general case of the calculus of variations gets a bit hazy: in particular I think that just saying that L = K - U and moving on when it wasn’t really necessary is sort of awkward. (I also do think it could do you some good to work on your audio editing a touch, since the volume and fidelity is a bit inconsistent, and some of the less necessary visual components are a bit eclectic)

I think you’ve got a lot of good stuff going on here, describing an interesting corner of math, and I do hope you keep it up. Take care!

I really liked the “aha” moment of the segment length going to zero denoting constant acceleration. The video would be better if the pacing was adjusted - it’s easy to briefly zone out and then get completely lost.

A visual introduction to the calculus of variations and motivation of Lagrangian mechanics.

It is a bit fast to follow in real time, but could be used by a student willing to pause frequently and work through the steps to gain an intuition for how variational problems work.