Finding the path of least action (part 1)

Рет қаралды 45,814

11 жыл бұрын

A derivation the the Euler-Lagrange equation using a specific set of coordinates. This video really just frames the problem.

Пікірлер: 31

@kvawnmartin1562 6 жыл бұрын

You did a much better job than my physics professor. Thank you

@roberth5435 8 жыл бұрын

"To first order" -- Leonard Susskind describes it this way: delta is such a small number that delta squared is zero. That way if delta is part of a Taylor series, we can simply ignore delta^2, delta^3, and so forth. Only the first order -- delta^1 -- counts. It is the first order.

@avion85 10 жыл бұрын

Fantastic! A very friendly and approachable intro to variational calculus. Always best to connect it to the real world...

@peternavakopp9105 9 жыл бұрын

Thanks, man. You've helped me prepare for my midterm exam tomorrow.

@karimkhan1312 8 жыл бұрын

east or west-- u r the best-- thank u sir

@parthabanerjee1234 5 жыл бұрын

What a nice way to teach! I truly appreciate it. Not many university professors are capable of teaching this way. But perhaps they did not learn it this way either. BTW, the Richard Feynman quote on your wall is also my favorite quote on Physics. Once more, thank you. :-)

@jjillinish 7 жыл бұрын

you sound just like ewan mcgregor from Fargo. Thanks for the great video!

@PhysicsHelps 10 жыл бұрын

Hey thanks for the kind words! I'm using a wacom bamboo tablet.

@HellaPerformance 10 жыл бұрын

Lol I disagree with aby neko. Your videos are super helpful, thanks :) Are you writing with a mouse?

@CHIVAC0LA 9 жыл бұрын

Thanks !

@paulsutton5896 4 жыл бұрын

In common with other explanations, the "action" makes use of the quantity: KE - PE. This is the bit that I don't understand. It seems so arbitrary - even if you end up with the equations which you want. You might as well throw in your inside leg measurement. I have tried to track this concept back to Lagrange, himself - short of reading Lagrange's original paper. I have a copy of Morris Kline's stupendous work: "Mathematical Thought from Ancient to Modern Times", OUP 1972. On page 588, the differential equations are given with a PLUS sign. Is this a printing error? At least this makes sense.

@quizzisation 10 жыл бұрын

I think potential energy is only a function of the position and nothing else, so U(xt) is ok and U(x') is wrong

@williejohnson1669 10 жыл бұрын

at the 7:48 mark you say T is a a function of dx/dt not x directly. So its T(dx/dt) ? And does this also pertain to U? i.e., instead of U((x)t) should it be U(dx/dt)?

@zmartin5335 9 ай бұрын

Hi, I see noone replied to you and I'm wondering the same thing. Do you know the answer, it's been 9 years :)

@ferencbucsky648 2 ай бұрын

@@zmartin5335 potential energy is only a function of position (x) while kinetic energy is a function of velocity(dx/dt) (U=m*g*h, T=1/2 mv^2)

@deconfinedQPT 7 жыл бұрын

Why T-V ?

@joeboxter3635 5 ай бұрын

Okay ... The IC point I give you. But how do you know what the end point is apriori? Newton only requires IC. In contrast this is a BVP and so requires more knowlege apriori to tell you the evolving physics.

@ollenmt1729 8 жыл бұрын

Are you from boston perhaps?

@PhysicsHelps 8 жыл бұрын

+Öllenm T Minnesota

@yuichilee96 8 жыл бұрын

+PhysicsHelps My Physics tutor during my A Levels was also from Minnesota!

@Husterization 4 жыл бұрын

watch at x1.5

@alexweeda2826 8 жыл бұрын

why don't you just use the set notation E their. all that you are talking about is sets.

@TheDavidlloydjones 7 жыл бұрын

It travels in an ellipse, not a parabola. It might travel in a parabola if the Earth were flat, though I can't see how gravity would work in a flat Earth of infinite size without having pulled you down to a thin layer of mush on its surface. If it weren't of infinite size, it wouldn't really be flat, would it? So you would have something in between an ellipse and a parabola. Fortunately, we know the answer. It's pretty close to round. Making your example elliptical really shouldn't interfere with the point you're making about calculating the Lagrangian. -dlj.

@PhysicsHelps 7 жыл бұрын

You're right. There's an unmentioned approximation that the gravitational field is completely uniform. If you're doing calculations out in space, you wouldn't want to do this, but for this example of throwing a rock into the air, it's an extremely good approximation (which is why it's used in every physics class with a sane teacher). Another interesting point is that there's nothing between an ellipse and a parabola. You can look up information on conic sections if you're curious about that. One more interesting point is that an infinite sheet of land with finite thickness wouldn't have an infinite gravitational pull. This calculation is usually done in the context of a charged plate in an electrostatics class, but the result applies to gravity as well.

@TheDavidlloydjones 7 жыл бұрын

Fizz, I stand corrected on the attaction, electrostatic or gravitational, of Infinit PlatWorld. On the ellipse question you are quite right that almost all high schools insist on imposing the ellipse on their long-suffering students. A very large majority of high school "teachers" believe the inane proposition that teaching something incorrect makes it simpler and easier to understand. What they miss with that stupidity is the opportunity to explain in thirty seconds flat the ver-ree valuable lesson that it's often necessary, useful, routine, sensible and decent to use an approximation. Among the students most don't know about Kepler, so the only thing they lose is the important lesson about the use of approximations. The minority who know the teacher is lying out of laziness or ignorance simply nod and carry on with slightly increased cynicism. That's the high school situation. I don't understand what you are saying about university students. By the time they hit a class like this they will know about Kepler for sure. What possible excuse can there be for carrying on with the dishonest version? Cheers, -dlj.

@PhysicsHelps 7 жыл бұрын

The approximation remains a good one when you get to university. And regardless of level, it's pedagogically useful to layer in complexity.

@TheDavidlloydjones 7 жыл бұрын

Yes, but the pedagogical point of the approximations are sometimes useful, as long as you are clear that they are not the real thing. If you simply pretend that it's *not* an approximation, then you are lying -- and teaching the very impressive lesson that teachers think that lying is usually the best thing to do. -dlj.

@Peter_1986 7 жыл бұрын

+David Lloyd-Jones "Lying"? What are you talking about? The whole reason why physicists make approximations is because it makes a lot of things much easier to deal with, and it won't make any meaningful difference. For example, if you were 30,000 feet above the surface of the Earth then your weight would be about 99.8% of your usual weight, which isn't exactly a dramatical difference - and that's also way higher than you would usually go in most dynamics problems that take place on Earth.