Derivation of Hamilton's Equations of Motion

Derivation of Hamilton's Equations of Motion | Classical Mechanics

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Күн бұрын

Hamilton’s equations of motion describe how a physical system will evolve over time if you know about the Hamiltonian of this system.
00:00 Introduction
00:12 Prerequisites
01:01 Derivation
01:47 Comparing Coefficients
02:27 Example
If you want to read more about the Lagrangian formulation of #ClassicalMechanics, we can recommend the book „Mechanics“ by Landau and Lifshitz:
amzn.to/2NjI8gQ
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Пікірлер: 67

@taimew3 5 жыл бұрын

How you've managed to condense this so clearly in just over 3 minutes is beyond me, and with an example too! Thanks for all your work!! :)

@PrettyMuchPhysics 5 жыл бұрын

That‘s the spirit of this channel, glad you liked it! :)

@2tehnik 3 жыл бұрын

Usually when I pick a short video for explaining a topic in math or physics I don't expect to get much. But this is pretty much exactly what it says on the cover, so props for that.

@PrettyMuchPhysics 3 жыл бұрын

That‘s exactly what we want to achieve with this channel, thanks for your nice feedback!

@user-cl8rt3xc2t 10 ай бұрын

Awesome work, never seen simpler explanation , thank you very much❤

@PrettyMuchPhysics 7 ай бұрын

Thank you :)

@ignacioedmundojaramillo6627 3 жыл бұрын

its impressive how clearly this video explains just what i was looking for. thank you so much

@PrettyMuchPhysics 3 жыл бұрын

You‘re welcome! Thanks for your nice words!

@JohanBesterphotos 5 жыл бұрын

Wow! No distracting background music. Clear-as-day writing on a pure white background. How did you do it? What tools did you use if I may ask?

@PrettyMuchPhysics 5 жыл бұрын

Thanks! We use an app called "Explain Everything"!

@yoel11612 5 жыл бұрын

Amazingly concise! Great derivation!

@PrettyMuchPhysics 5 жыл бұрын

Thank you! 😃 That’s what we’re aiming for with our videos!

@naturematters08 4 жыл бұрын

learned about the hamiltonian from you in 3 minutes vs other places in multiples of 3 hours

@PrettyMuchPhysics 4 жыл бұрын

That‘s so great :D Thanks for watching!

@ebukammaduekwe392 3 жыл бұрын

Wow, I can't believe I understood this whole course in a 3 mins video

@PrettyMuchPhysics 3 жыл бұрын

😁

@manjeetchahal5548 3 жыл бұрын

You produce really amazing content: covering the concept in very effective way.

@PrettyMuchPhysics 3 жыл бұрын

Thanks for your nice comment! We do our best!

@matthewheadley9172 2 жыл бұрын

@@PrettyMuchPhysics ❤️

@biswajeetpattnayak4921 2 жыл бұрын

Great video all are done within 3 minutes with example thank u💫

@PrettyMuchPhysics 2 жыл бұрын

Thanks for your nice comment!

@davidenatale5956 5 жыл бұрын

You saved my life, thank you man

@PrettyMuchPhysics 5 жыл бұрын

Anytime :D

@jidhinm.s4430 5 жыл бұрын

No wrds to say sir....thank you soo much for making me understand hamiltonian very clearly within a short time🥰🥰🥰😍😍😍

@beoptimistic5853 3 жыл бұрын

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@addas1392 4 жыл бұрын

Clear as bright sunshine. Thanks a lot.

@beoptimistic5853 3 жыл бұрын

kzfaq.info/get/bejne/jrd5ldFjnMqzmnk.html 💐

@user-pk6vy8lj1s 8 ай бұрын

Great video. I would like to know how the partial derivative of H with respect to q dot gives Pdot. Should it not be just P ?

@jsconventschooldallaobraso6222 2 жыл бұрын

Awesome teaching style

@PrettyMuchPhysics 2 жыл бұрын

Thank you very much! 🙂

@itsanna123 4 жыл бұрын

Hey! You are awesome. Thank you for this.

@PrettyMuchPhysics 4 жыл бұрын

YOU are awesome for watching it, thank you!

3 жыл бұрын

I love your videos. Thanks a lot. Btw which software or application do you use for writing these notes?

@PrettyMuchPhysics 3 жыл бұрын

Thank you! We use an iPad app called „Explain Everything“!

3 жыл бұрын

@@PrettyMuchPhysics Thanks!

@kieranmurray7373 Жыл бұрын

This is just brilliant.😅

@prityverma2028 3 жыл бұрын

Thanks a lot🙏 My all doubt has cleared

@PrettyMuchPhysics 3 жыл бұрын

That‘s great! Thanks for watching!

@RachidOUSALEM 3 жыл бұрын

جميل جداا 😍😍😍 شكراا جزيلا...

@briann10 3 жыл бұрын

this channel is way too underrated

@PrettyMuchPhysics 3 жыл бұрын

Thanks for watching and helping us grow! :D

@waynelast1685 3 жыл бұрын

Very nice. One gets two first order equations using H , but also using L ( lagrangian) if you use the Euler-Lagrange equations. The only difference is you need to know H in the former case, and L in the latter. When is it more advantageous to use L rather than H? I know H is easy to find sometime when you have a conservative system because H is simply the total energy = kinetic plus potential energy. So maybe if a conservative system does not exist one may prefer , or should , use L ?

@PrettyMuchPhysics 3 жыл бұрын

If there are a lot of symmetries in your system, then L is more useful, since it directly exhibits those symmetries. That's for instance why the Standard Model of particle physics is build using a Lagrangian, because it's more straight-forward to implement all the symmetries.

@bassitorikos5292 5 жыл бұрын

i relly like it thnx

@Laibakhan-cf7rb 5 жыл бұрын

it's helpful thanx sir

@beoptimistic5853 3 жыл бұрын

kzfaq.info/get/bejne/jrd5ldFjnMqzmnk.html 💐

@johannesmoerland5438 3 жыл бұрын

If the partial time derivatives of the hamiltonian and the lagrangian cancel out, doesn't that imply that the partial time derivative of (p*q•) has to be zero?

@PrettyMuchPhysics 3 жыл бұрын

That's correct!

@KlaudiusL 4 жыл бұрын

Liked & subscribed 👍

@PrettyMuchPhysics 4 жыл бұрын

😄

@m.bhuvaneswari256 4 жыл бұрын

Thankyou👌

@beoptimistic5853 3 жыл бұрын

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@ArthurMorganFTW_RDR 4 жыл бұрын

Best decision I made after spring break watching this video..................

@PrettyMuchPhysics 4 жыл бұрын

Great decision indeed!

@ArthurMorganFTW_RDR 4 жыл бұрын

@@PrettyMuchPhysics Hey I really appreciate your effort, hard to find someone explaining hamiltonian mech in this straight forward way nowadays.

@PrettyMuchPhysics 4 жыл бұрын

Thanks for the kind words! Stay tuned for many more videos to come!

@consciousness147 5 жыл бұрын

Danke!!

@PrettyMuchPhysics 5 жыл бұрын

Gerne! :)

@consciousness147 5 жыл бұрын

@@PrettyMuchPhysics mehr Theo mechanik bitte 🤗

@PrettyMuchPhysics 5 жыл бұрын

Theoretische Mechanik ist ja ein riesiges Feld, da werden wir sicher noch spannende Themen finden ;)

@consciousness147 5 жыл бұрын

@@PrettyMuchPhysics Mein vorschlag wäre mehr mit hamiltons prinzip, was wirkungsfunktional und variations rechnug ist 😍

@daydream2190 2 жыл бұрын

I don't understand the transformation between H and L

@PrettyMuchPhysics 2 жыл бұрын

This is called a Legendre transformation (en.wikipedia.org/wiki/Legendre_transformation). Aside from the mathematical details, we can use it to switch from L to H and back.