# Read about euler lagrange equation | 17 Discussions | Page 1

6. ### Geodesics and Motion in an EM Field

I've also attached my attempt as a pdf file. My main issue seems to be I only get one A partial term. Any help would be appreciated.
7. ### The Lagrangian for a piece of toast falling over the edge of a table

First of all, disclaimer: This isn't an official assignment or anything, so I'm not even sure if there is a resonably simple solution. Consider the following sketch. (Forgive me if it isn't completely clear, I didn't want to fiddle around for too long with tikz...) Let us assume that we can...
8. ### Find the curve with the shortest path on a surface (geodesic)

Homework Statement Let ##U## be a plane given by ##\frac{x^2}{2}-z=0## Find the curve with the shortest path on ##U## between the points ##A(-1,0,\frac{1}{2})## and ##B(1,1,\frac{1}{2})## I have a question regarding the answer we got in class. Homework Equations Euler-Lagrange ##L(y)=\int...
9. ### I Total Derivative of a Constrained System

Hi all, I was working on a problem using Euler-Lagrange equations, and I started wondering about the total and partial derivatives. After some fiddling around in equations, I feel like I have confused myself a bit. I'm not a mathematician by training, so there must exist some terminology which...
10. ### Proving Snell's law using Euler-Lagrange equations

Homework Statement Prove that snell's law ## {n_1}*{sin(\theta_1)} ={n_2}*{sin(\theta_2)} ## is derived from using euler-lagrange equations for the time functionals that describe the light's propagation, As described in the picture below. Given data: the light travels in two mediums , one is...
11. ### A Maximization problem using Euler Lagrange

Hi, I'm trying to solve the following problem ##\max_{f(x)} \int_{f^{-1}(0)}^0 (kx- \int_0^x f(u)du) f'(x) dx##. I have only little experience with calculus of variations - the problem resembles something like ## I(x) = \int_0^1 F(t, x(t), x'(t),x''(t))dt## but I don't know about the...
12. ### I Rigorously understanding chain rule for sum of functions

In my quest to understand the Euler-Lagrange equation, I've realized I have to understand the chain rule first. So, here's the issue: We have g(\epsilon) = f(t) + \epsilon h(t). We have to compute \frac{\partial F(g(\epsilon))}{\partial \epsilon}. This is supposed to be equal to \frac{\partial...
13. ### I Help a novice with EL equation derivation

Hello everyone, Reading Landau and Lifshitz Course of Theoretical Physics Volume 1: Mechanics (page 3) I got suck in the following step (and I cite in italics): The change in S when q is replaced by q+δq is \int_{t_1}^{t_2} L(q+δq, \dot q +δ\dot q, t)dt - \int_{t_1}^{t_2} L(q, \dot q, t)dt...
14. ### Pendulum oscillating in an accelerating car

We have a car accelerating at a uniform rate ## a ## and a pendulum of length ## l ## hanging from the ceiling ,inclined at an angle ## \phi ## to the vertical . I need to find ##\omega## for small oscillations. From the Lagrangian and Euler-Lagrange equations, the equation of motion is...
15. ### I Equivalent Klein-Gordon Lagrangians and equations of motion

Suppose one starts with the standard Klein-Gordon (KG) Lagrangian for a free scalar field: $$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^{2}\phi^{2}$$ Integrating by parts one can obtain an equivalent (i.e. gives the same equations of motion) Lagrangian...
16. ### I Applying Euler-Lagrange to (real) Klein-Gordon Lagrangian

I'm currently studying Quantum Field Theory and I have a confusion about some mathematics in page 30 of Mandl's Quantum Field Theory (Wiley 2010). Here is a screenshot of the relevant part: https://www.dropbox.com/s/fsjnb3kmvmgc9p2/Screenshot%202017-01-24%2018.10.10.png?dl=0 My issue is in...
17. ### B Euler-Lagrange equation for calculating geodesics

Hello I am little bit confused about lagrange approximation to geodesic equation: So we have lagrange equal to L=gμνd/dxμd/dxν And we have Euler-Lagrange equation:∂L/∂xμ-d/dt ∂/∂x(dot)μ=0 And x(dot)μ=dxμ/dτ. How do I find the value of x(dot)μ?