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The Euler-Poincare equation

Can anyone tell me very basically how the Euler-Poincare equation generalises the Euler-Lagrange equation? Further does anyone know if there is an "easy" relationship between the two, i.e. can anyone ...
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Total Vs Partial in Lagrange density?

I have a question regarding the red term below. This is the integration by parts during the derivation of the Euler-Lagrange equation for continuous systems. Why is this not the time derivative ...
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Assuming we have a Effective Field Theory, for example a Real Scalar Field Theory, defined through a Lagrangian density of the form $\mathcal{L}_{eff} = \frac{1}{2}\partial_\mu\phi \partial^\mu\phi - ... 2answers 107 views Classical Field Theory - Continuum limit in forming the Lagrangian density and the elasticity modulus I have been looking at taking the continuum limit for a linear elastic rod of length$l$modeled by a series of masses each of mass$m$connected via massless springs of spring constant$k$. The ... 0answers 40 views Treating$\psi$and$\psi^{*}$as independent variables when varying the action [duplicate] Consider the following Lagrangian (deinsity): $${\mathcal{L}} = \partial_{\mu}\psi^{*} \partial^{\mu}\psi - V(|\psi|^2)$$ In my notes it says that " it's easier (and equivalent) to treat$\psi$and ... 0answers 30 views Equations of motion with replacing the Lagrangian by irrep diagrams generating functional I have read that equations of motion of ghosts is equal to $$\tag 1 \frac{\delta \Gamma}{\delta \bar{c}^{a}(x)} = -\partial^{\mu}_{x}\frac{\delta \Gamma}{\delta K^{\mu , a}(x)},$$ where$\Gamma = W ...
In an essay I am reading on celestial mechanics the equations of motion for a 2 body problem is given as: $$\mathbf{r}''=\nabla(\frac{\mu}{r})=-\frac{\mu \mathbf{r}}{r^3}$$ Fine. Then it says the ...