Hamiltonian Mechanics in 10 Minutes

In this video I go over the basics of Hamiltonian mechanics. It is the first video of an upcoming series on a full semester university level Hamiltonian mechanics series.

Corrections

-4:33 the lagrangian should have a minus sign between the first two terms, not a plus.

[KevinToppenberg]

Thank you for making this video. I have been looking for an introductory level video about Hamiltonian mechanics, and this filled the gap. You have put a lot of effort in the animation, and it really adds to the presentation. To make this even better, I would recommend working on the pacing of the animation. There were many times that things would be shown on the screen, only to flash away before I could absorb what was being shown. So I would have to pause or rewind. Overall, you have done a great job. Keep up the great work!

[boshrabesharatian]

It was the most fluent way of explaining Hamiltonian Mechanics I've ever seen. As a biginer, I appreciate this basic videos a lot. Thanks 🙏

[chillaxiommath]

I just now understand what a phase state is for the first time! Thanks a bunch!

[aneikei]

Your video is awesome! Well done. You take what could be considered a complex subject and break it down into simple concepts. Keep up the good work.

[MrSomethingdark]

Omg! Thank you so so much my dude. So many important points mentioned here. As someone who has never learned it and is doing it now this really shows the ins and outs. Great contrast between them too!

[TheVictorsuvorov]

thank you so much. this is the best explanation i have seen so far

[sergio]

Hello! Not using Newton's F = ma, allow me ask:
1 - Where does the { Action = Integral (K - U)dt} come from?
2 - Where does the {Lagrangian (K - U)} come from?
3 - Can I deduce that I must minimize the Action integral equation from minimizing the potential energy U?
4 - Can you elaborate?
Thanks!👋

[DannyWrigley]

Very helpful thanks man. Laughed out loud at Lagrange’s speech bubble too 😂

[letsbegood_]

This was truly helpful, your explanation was precise and great. Thanks a lot sir!

[dirkjensen]

Great video mate, nice comparison between Newtonian, Lagrangian and hamiltonian on the same problem. Thanks for making it!

[simon-xicv]

Very good explanations and animation. Thanks for the video!

[Crayonchn]

Omg this helped me so much! Thank you for this! 😭✨

[spencerknight]

This is a really well made video, I would just recommend slowing down while you speak and this will be perfect.

[tomkerruish]

Wouldn't the phase space for two particles be twelve-dimensional? Each has three apiece for position and momentum, so 3+3+3+3 = 12.

[ianirvingthorsonc]

Aaaa loved the "language" part...just like religions are different languages, not different things..speak English, Spanish, math, hamiltonian, lagrangian, newtonian, catholic, christian, budism, zen etc etc❤

[justinparisien]

great vid! lets get rid of those gay forces😂

[PetakyahBuckley-htiz]

That formula is longer than the alphabets

[afterglow]

Can we say that water is H2O?, all you have to do is cross the mexican border and over there is AQUA.

[sleepycritical]

You got a stutter and a slur bro, it’s not a major problem but I think you should speak slower and in a more sound isolated room, with a good mic with a wind protector so that you can much more easily edit and re record some lines.

An isolated room because you need to be able to control the environment to ensure the quality of the recording is consistent over all takes.

Some suggestions is to split the script by sentences and punctuation, record up to a comma or a period. Add an EQ to get rid of the low frequencies and you’re good to go.

Now not all stutters are bad, I find it quite endearing, adds character, but some lines should be re recorded.

Other than that I like the explanation it’s very intuitive.

[ihbarddx]

You didn't teach me Hamiltonian Mechanics in 10 minutes, I'm embarrassed to say. As Kevin Toppenberg pointed out, the things you flash onto the screen require a great deal more development to make this work. BTW, in Principia, Newton's actual second law is F=Delta(MV) - which is to say, the force (vis) Newton defines in his second law is what we now call impulse. (He defines motion as momentum, and a force is an action that changes a body's motion, so the quantity of force is the change in momentum - not the rate of momentum change. F=m*a is revisionism.) Therefore, real Newtonian mechanics may be closer to Hamiltonian mechanics than we are ready to admit.