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Questions tagged [euler-lagrange-equation]

In calculus of variations, the Euler–Lagrange equation, Euler's equation, or Lagrange's equation, is a second-order partial differential equation whose solutions are the functions for which a given functional is stationary.

In calculus of variations, the Euler–Lagrange equation, Euler's equation, or Lagrange's equation, is a second-order partial differential equation whose solutions are the functions for which a given functional is stationary. Reference: Wikipedia.

It was developed by Swiss-Russian mathematician Leonhard Euler and French-Italian mathematician Joseph-Louis Lagrange in the 1750s.

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Differentiating a Lagrangian in the Euler-Lagrange equation

I am currently working with an appropriate Lagrangian $L=\frac{1}{2m}(m\overrightarrow{v}+\frac{q}{c}\overrightarrow{A})^2-(\frac{q^2}{2mC^2})\overrightarrow{A}\cdot \overrightarrow{A}-q\phi$ I am trying to apply the Euler Langrange equation to…
darren
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Double pendulum - angles

I am a student who is very new to mechanics. I have to calculate the Euler-Lagrangian equation for a double pendulum, which is okay. But the angle of the the second pendulum is measured with respect to the first pendulum, and not the vertical. In…
Theoryofmech1912
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Time Derivative

Found Lagrange Equation $$E = 2F\ddot q + \frac{dF}{dq} + \frac{dv}{dq} $$ knowing that Equation for Total energy is E = T + v $$E = 2F\ddot q + \frac{dF}{dq} - \frac{dv}{dq} $$ Is that correct? ( change of signs? ) How would i find Time derivative…
Unknownstarz
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Minimisation problem in 2D with Dubois-Reymond, deriving the Euler-Lagrange equation and natural boundary conditions. Confusion over the latter.

I find I am confused about the `natural' boundary conditions of this problem. I will first formulate the problem, the method in which I find my final result so far, and then I will state my confusion more clearly. In short, the confusion is that the…
Daimonie
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How resolve Lagrange equation ?

How I can resolve this taks? I complety green in differential equations $y = xy' +y'^5$
Svs
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