I have been WAITING FOR SO LONG just to see you make a video on Lagrangian mechanics. It really is a fascinating concept in classical mechanics and the fact that it doesnt concern any forces is why i like it! Keep teaching much more advanced concepts such as these!
You should show how this is equivalent to Newtonian mechanics. Here is the example of a single particle in an arbitrary potential, in one dimension (you can generalise this to n particles in n dimensions too!). A single particle has kinetic energy 1/2 mv^2, and let the potential be given by U: L = T - U = 1/2 mv^2 - U Hence, plugging this into the Euler Lagrange Equations: d/dt (∂L/∂v) = ∂L/∂x d/dt (∂/∂v 1/2mv^2 - U) = ∂/∂x (1/2mv^2 - U) d/dt (mv) =- ∂U/∂x ma = F F = ma
I once derived the pendulum equation using some trigonometry. Later, I derived the pendulum equation again just using Lagrange's equation and the magic happened. Lagrange's equation is so convenient sometimes, I call it the Lagrange hack HA!
That surprises me a lot. Why ban an elegant way of solving problems in which a lot of higher physics is based on. 🤔 Lagrangian Mechanics only really helps in systems of many particles mostly.
Is the way you actually find (by find i mean how did people come up with the equation) the euler lagrange equation just abusing the fact that using some partial differentiation rules LHS=RHS? it's not an intuitive thing, just purely mathematical?
there is a very deep and cool derivation. Fun preview: anytime we can apply the Euler Lagrange equation, we are choosing a path that minimises the Lagrangian over time. This is the principle of least action.
Will do! I initially started making it though, but decided to change my approach and show how it works first with familiar examples. I will also show some very complicated but beautiful examples very soon too!
Good question, forces are very intuitive. We can sort of see the mechanics of how they work. The Euler Lagrange equation works on minimising the integral of a non-measurable quantity, integrating with respect to time and using a partial differential equation. Might be a very interesting experiment to see how crazy Newtonian physics might look like, had you started out with Lagrangians. Interestingly though in higher level physics most laws of physics are summarised in Lagrangians as it's a concise way of summarising the entire physics in a single law with scalar quantities only.
This is a random question, but ages/levels are international physics olympiads for?, As the content in the papers seem to include complex calculus, it seem very different compared to physics alevel
good question. It is aimed at high school students by the international definition, i.e. most students that go there are around 17/18. Very different but highly demanding. The UK just won the top spot I believe in the International Astronomy Olympiad though and it shows it can absolutely be achieved : )
Hi, I do AQA a level physics and I wanted to ask if I can do past papers from different exam boards and old spec papers. I’m asking because I don’t want to ruin my technique
Next step - apply this to a HARD Problem: ua-cam.com/video/AAHt5gTNcM4/v-deo.htmlsi=SSsmQXTeqXwD6acm
I have been WAITING FOR SO LONG just to see you make a video on Lagrangian mechanics. It really is a fascinating concept in classical mechanics and the fact that it doesnt concern any forces is why i like it! Keep teaching much more advanced concepts such as these!
Thank you so much! Actually double pendulum coming up very soon and derivation of the Euler Lagrange equations.
You should show how this is equivalent to Newtonian mechanics. Here is the example of a single particle in an arbitrary potential, in one dimension (you can generalise this to n particles in n dimensions too!).
A single particle has kinetic energy 1/2 mv^2, and let the potential be given by U:
L = T - U
= 1/2 mv^2 - U
Hence, plugging this into the Euler Lagrange Equations:
d/dt (∂L/∂v) = ∂L/∂x
d/dt (∂/∂v 1/2mv^2 - U) = ∂/∂x (1/2mv^2 - U)
d/dt (mv) =- ∂U/∂x
ma = F
F = ma
excellent comment
This channel is so underrated
thank you so much for the kind comment!
How do you find Lagrangian Mechanics? Let me know!
it was interesting
@@himanshudahal5581 thanks for the comment
Please upload more of these kind of videos ❤❤😊
Please Make a video on Hamiltonian also
Excellent point, maybe even solve the same problem with Newtonian, Lagrangian and Hamiltonian Mechanics
That would be an amazing video !
I once derived the pendulum equation using some trigonometry. Later, I derived the pendulum equation again just using Lagrange's equation and the magic happened. Lagrange's equation is so convenient sometimes, I call it the Lagrange hack HA!
I know the feeling! I think I will post the double pendulum next which is basically a beast to solve without Lagrangians
@@zhelyo_physics cool! I can’t wait for your next video!
In indonesia National Science Olympiad, using lagrangian method in solving physics problem has been banned
That surprises me a lot. Why ban an elegant way of solving problems in which a lot of higher physics is based on. 🤔 Lagrangian Mechanics only really helps in systems of many particles mostly.
Very Clear explanation!
Thank you! Much appreciated!
Is the way you actually find (by find i mean how did people come up with the equation) the euler lagrange equation just abusing the fact that using some partial differentiation rules LHS=RHS? it's not an intuitive thing, just purely mathematical?
there is a very deep and cool derivation. Fun preview: anytime we can apply the Euler Lagrange equation, we are choosing a path that minimises the Lagrangian over time. This is the principle of least action.
I never study rotational mechanics so I have a question.
is moment of inertia a tensor?
Please make a video explaining the philosophy behind the lagrangian
Will do! I initially started making it though, but decided to change my approach and show how it works first with familiar examples. I will also show some very complicated but beautiful examples very soon too!
Why dont people generally use/teach the Lagrangian in high school and college mechanics?
Good question, forces are very intuitive. We can sort of see the mechanics of how they work. The Euler Lagrange equation works on minimising the integral of a non-measurable quantity, integrating with respect to time and using a partial differential equation. Might be a very interesting experiment to see how crazy Newtonian physics might look like, had you started out with Lagrangians.
Interestingly though in higher level physics most laws of physics are summarised in Lagrangians as it's a concise way of summarising the entire physics in a single law with scalar quantities only.
@@zhelyo_physics Woww, this was far more interesting than I thought would be😍😍
Thank you very much for the comment! It is! : ) @@debtanaysarkar9744
sir what we will replace whole newtonian meachincs with this lagrangion machenics without any issue?
You can express every single problem with both formulations. Problems with 1 object are typically much better suited for Newtonian mechanics though.
This is a random question, but ages/levels are international physics olympiads for?, As the content in the papers seem to include complex calculus, it seem very different compared to physics alevel
good question. It is aimed at high school students by the international definition, i.e. most students that go there are around 17/18. Very different but highly demanding. The UK just won the top spot I believe in the International Astronomy Olympiad though and it shows it can absolutely be achieved : )
You should be a university professor to be honest…. Your explanations are too good for a college teacher!!
thank you so much for the kind comment. Teaching is my passion : )
Hi, I do AQA a level physics and I wanted to ask if I can do past papers from different exam boards and old spec papers. I’m asking because I don’t want to ruin my technique
I think this is excellent practice, the physics doesn't change. Actually sometimes I have come across similar questions across different exam boards.
wtf
Chuj mnie przeraża
This sounds fake
all the best physics does : )