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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...

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Answer 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 +...

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How to linearise on Lagrangian level?

Consider a Lagrangian density$$\mathcal{L}(\phi, \nabla \phi) = \frac{1}{2} \, g^{\mu \nu} \, \partial_{\mu} \phi \; \partial_{\nu} \phi + V(\phi) \tag{1}$$The equation of motion (EOM), i.e. the...

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Answer 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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