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Comment by siddboots | Hacker News Reader

From another point of view, the lectures are purely focused on giving an intuition behind concepts in modern theoretical physics, which is only a very small part of what is taught in an undergraduate program.

Lagrangians are a difficult, and abstract concept, but they doesn't mean that they can't be communicated in 3-4 hours by a skilled educator.

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Agreed that these are geared towards intuition. Though for reference: in my undergraduate degree, Lagrangian Dynamics and Hamiltonian Dynamics were each given semester long treatments.

That's interesting. In my undergraduate degree (which I believe to be fairly standard for the US), Lagrangian and Hamiltonian dynamics were both part of a one-semester classical mechanics course, along with much else. I'm quite envious, though---both Lagrangian and Hamiltonian dynamics are beautiful, and I need a better background.

If you don't mind my asking, where did you do undergrad?

The University of Edinburgh, Scotland. They were two of my favourite courses, I was amazed at how simple some classes of problems became with the techniques. You should be able to find the course notes somewhere, but I'm not sure if they'd be much value without the lectures.

Ditto for me, though we spent quite a bit of time on Lagrangians and Hamiltonians in that semester.

For the 300-400 page version see: "Classical Mechanics" by Goldstein. I highly recommended this book. The first four chapters are a solid treatment of everything you learned in first year physics. For example, you will understand that the angular velocity \omega is actually \vec{\omega}.

Okay, so the gist of the whole Hamiltonian/Lagrangian is you we can solve problems by using energy calculations. The //Hamiltonian// describes the total energy in a system H = K + V. The Lagrangian is a bit f-up because, apparently, all the information you will ever need about the system can also be computed[1] from the Lagrangian L = K - V. The relation between H and L is called the Legendre transformation.

But the fun doesn't stop there. We have three different ways to solve physics problems until now (1) Newton (dynamics->a->kinematics), (2) Lagrangian + L-eqns, and (3) Hamiltonian + H-eqns. You would think physicists would stop at this point. Be like "OK we got three now, done!", but no they thought of an even more general way to think about the world.

The Hamilton-Jacobi equation is the final piece of the classical mechanics puzzle. In the last three chapters of Goldstein, you will learn about the connection between the Hamilton-Jacobi and Schrodinger's equation. Essentially, if you take the limit $\hbar \to 0$ in the main equation of QM, it simplifies to the Hamilton-Jacobi equation. Read JJ.Sakurai's ``Modern QM'' to continue.

[1] http://en.wikipedia.org/wiki/Hamiltonian_mechanics#Calculati...

[2] http://en.wikipedia.org/wiki/Hamilton%E2%80%93Jacobi_equatio...

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