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Results tagged with lagrangian-formalism
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user 220348
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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Motivation behind action when deriving ''Strings as Harmonic oscillators" in Zwiebach's book...
Page 248 gives us this action and he simply says that we will assume it correct.
$$
S=\int d \tau d \sigma ~\mathcal{L}=\frac{1}{4 \pi \alpha^{\prime}} \int d \tau \int_{0}^{\pi} d \sigma\left(\dot{X …
- 99
-1
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Motivation behind action when deriving ''Strings as Harmonic oscillators" in Zwiebach's book...
$$
\delta S=\int_{\tau_{i}}^{\tau_{f}} d \tau\left[\delta X^{\mu} \mathcal{P}_{\mu}^{\sigma}\right]_{0}^{\sigma_{1}}-\int_{\tau_{i}}^{\tau_{f}} d \tau \int_{0}^{\sigma_{1}} d \sigma \delta X^{\mu}\lef …
- 99