Answer by ZeroTheHero for How to linearise on Lagrangian level?
Normally you would expand about a fixed point where $V$ is extremum but, if not suppose a point particle in 1d as an example:$$L= \tfrac12 m \dot{x}^2 - (V_0+A x + \tfrac12 k x^2)\, .$$The EOM for this...
View ArticleAnswer by hft for How to linearise on Lagrangian level?
Consider a Lagrangian density$$\mathcal{L}(\phi, \nabla \phi) = \frac{1}{2} \, g^{\mu \nu} \, \partial_{\mu} \phi \; \partial_{\nu} \phi + V(\phi) \tag{1}$$... Assume now that $\phi = (\phi_0 +...
View ArticleHow to linearise on Lagrangian level?
Consider a Lagrangian density$$\mathcal{L}(\phi, \nabla \phi) = \frac{1}{2} \, g^{\mu \nu} \, \partial_{\mu} \phi \; \partial_{\nu} \phi + V(\phi) \tag{1}$$The equation of motion (EOM), i.e. the...
View ArticleAnswer by Andrew for How to linearise on Lagrangian level?
The underlying motivation for linearizing an equation of motion is that you are looking for small deviations to a known solution of the full equations of motion. The approximation is valid so long as...
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