Derivation of Hamilton's Equations of Motion | Classical Mechanics

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:
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[taimew]

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!! :)

[tehnik]

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.

[عبدالرءوفالأطرش]

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

[ignacioedmundojaramillo]

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

[ebukammaduekwe]

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

[naturematters]

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

[biswajeetpattnayak]

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

[jidhinm.s]

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

[manjeetchahal]

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

[ArthurMorganFTW_RDR]

Best decision I made after spring break watching this

[JohanBesterphotos]

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?

[addas]

Clear as bright sunshine. Thanks a lot.

[waynelast]

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 ?

[prityverma]

Thanks a lot🙏
My all doubt has cleared

[itsanna]

Hey! You are awesome. Thank you for this.

[EbituUkiwe-ff]

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
?

[johannesmoerland]

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?

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

[daydream]

I don't understand the transformation between H and L