Euler-Lagrange Equation

Video showing the Euler-Lagrange equation and how we can use it to get our equations of motion, with an example demonstrating it.

[Peter_]

Finally someone who actually explains the Euler-Lagrange equations.
Every time I search for anything relating to Lagrangian mechanics I just get "Lagrangian Multipliers" for some reason.

[NA-udqm]

Thank you for explaining this. First time working with Euler-Lagrangians and this example helps tremendously.

[franklinjuarez]

Beautiful explanation, you bring a complex equation and concept into a very well known fact. I was looking for something like this.

[blakethephysicist]

Excellent video, one of the best talks on the Euler-Lagrange equation that I've found. One question: it's probably easy to decipher from context, (i.e. examining the equations and seeing which variable also has a dot-variable/first derivative) but how exactly does one know which variable takes the place of the generic "q" and "q-dot" in different systems? Thanks in advance.

[DeborahEdelen]

Thanks a lot, you made Leonhard Euler, AND Leonard Susskind, clearer!

[arcy]

I love you?? this was so well explained, I understood it at the first try and I was like. mindblown

[ssss-mnsf]

May I ask a question?
At 2:45, when calculating the partial derivative of L with respect to y,
why is it appropriate to consider [ y dot ] as a constant?
Since the velocity of the dropped ball (= y dot) is [ - gravitational acceleration × time]
and the height of the dropped ball ( = y ) is [ initial height - (1/2 × gravitational acceleration× (time^2) ) ],
it seems possible to express [y dot] in terms of [y].
Considering that the value of [ y dot ] is not independent of [ y ], it seems unclear whether it should be treated as a constant.
Additional instructions about this would be greatly appreciated.

[bridge]

Thanks for showing an example of deploying the Euler-Lagrange equation in solving a model problem.
By the way, why did you not apply chain rule while taking partial time-derivative of Lagrangians, e.g. could the first lagrangian be -
del_L / del_y = m ⋅ y_dot ⋅ (del_y_dot / del_y) -mg

If not, then, is it because you are taking two variables y_dot and y as being independent varibles?