# Tagged Questions

For questions involving the Lagrangian formulation of a dynamical system. Namely, the application of an action principle to a suitably chosen Lagrangian or Lagrangian Density in order to obtain the equations of motion of the system.

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### Lagrangian density for the electromagnetic field

I want to know how the Lagrangian density for the electromagnetic field is written in the following form:
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I asked a more general question earlier about the Routhian, but I'm still having trouble working with it. Here's my specific case. Given the following Lagrangian: $$L=(1/2)m(\dot{r}^{2}+r^{2}\dot{\... 4answers 822 views ### Are Lagrangians and Hamiltonians used by Engineers? Analytical Mechanics (Lagrangian and Hamiltonian) are useful in Physics (e.g. in Quantum Mechanics) but are they also used in application, by engineers? For example, are they used in designing bridges ... 1answer 205 views ### Definition of Kinetic energy In class we had that  T= \frac{1}{2}T_{ij}v_iv_j where we used the Einstein summation convention. Hitherto we only discussed examples where the kinetic energy was dependent of the square of one ... 2answers 641 views ### Different approaches to calculating the Christoffel symbols I would be very grateful to whoever can debug the following calculations... We have the metric for static spacetime:$$ds^2 = -\exp(2U(\vec x))dt^2+h_{ij}(\vec x) d x^i d x^j$$I want to find the ... 3answers 401 views ### Is the path of stationary action unique? What are the physical implications of L_{\dot{x}}=L_x Below, for any function Q the notation Q_x means \frac{\partial Q}{\partial x}, and Q_{xx} means \frac{\partial^2 Q}{\partial x^2}. In physics, the trajectory of a particle is given by the ... 1answer 143 views ### Obtaining the conserved current of the Lagrangian making the parameter depending on x To calculate the conserved current due to an internal symmetry of the system (expressed by the Lagrangian density) we can proceed as follows: if it is invariant under \delta \phi = \alpha \phi, ... 1answer 429 views ### Euler-Lagrange Equation with logarithmic potential A particle moving towards the origin has initial conditions x(t=0) = 1 and \dot{x}(t=0)=0. If the Lagrangian is$$L:=\frac{m}{2}\dot{x}^2 -\frac{m}{2}\ln|x|$$This should satisfy Euler ... 1answer 274 views ### Relationship between local and global scaling (Weyl) symmetry Theorem 5.1 on page 80 of this paper says that Assuming that the matter fields satisfy their equations of motion, the matter field action is locally Weyl invariant if and only if the corresponding ... 2answers 264 views ### Is the gravitational constant G a minimum value in some sense? Assume a central body of mass M, and call a the acceleration of a test body at a distance r due to any interaction whatsoever with the central body. Is is correct to say that the ratio a r^2/ M... 1answer 291 views ### Do Lagrangian points actually maintain a fixed distance? I was reading on up Lagrangian points and the restricted three-body problem. From what I was able to tell, the Lagrangian points are 5 points in a two-body system such that a third body would be ... 2answers 800 views ### M-theory no lagrangian? Is there any formulated lagrangian (density) for M-theory? If not, why is there no lagrangian? If not, is this related to many vacua existing? Thnx. 1answer 546 views ### Origins of the principle of least time in classical mechanics Is it possible to derive the principle of least time from the principle of least action in lagrangian or hamiltonian mechanics? Or is Fermat's principle more fundamental than the principle of least ... 1answer 35 views ### My Hamiltonian for a light ray vanishes I have the following issue with understanding. A light ray traveling from q(\tau_1) to q(\tau_2) minimizes the integral \int\limits_{\tau_1}^{\tau_2} n(q(\tau))|\dot{q}(\tau)| d\tau, so the ... 2answers 72 views ### Where is the BRST symmetry? When quantizing YM we start from the gauge fixed path integral (to remove redundancy of integrating over Gauge symmetric configurations)$$\int \mathcal{D}A \delta(G(A)) \text{det} \Delta_{FP}e^{i\int ...
I am trying to understand if the deterministic 2+1D Kuramoto-Sivashinsky equation $$\partial_t h = -\nu \nabla^2 h - K \nabla^4 h + \frac{\lambda}{2} (\nabla h)^2,$$ where $\nu$, $K$, $\lambda$ ...