Can anyone explain to me how Jackson goes from equation 5.20 to 5.21 (Magnetostatics - Derivation of the curl of B in terms of the current density).
He says that he's used integration by parts but I cant see how he got rid of the first term (the one that involves integrals only) when...
Sorry for saying that its a number but I still didn't get it. And I think I basically want to know how can Lagrangian the function be transformed into Lagrangian the matrix. e.g. we have 2L = \dot{\eta}^T m \dot{\eta} - \eta^T v \eta . But the \eta are essentially column vectors, giving me a...
I wondered whether that was the case. However, this being celestial mechanics, it is obvious that the potential is not constant. In fact, only one or two lines down, the energy is written as a sum of KE and Potential (as you would expect)
Are the principle of least action(see first equation) and the hamilton principle 'exactly' the same? As far as I know, yes. How do I go from one to the other
My Graduate Mechanics text (Walecka and Fetter) says in the chapter on Small Oscillations, that the Modal Matrix Diagonalizes the Lagrangian
L = \sum_{\sigma=1}^\infty (\dot{\zeta_\sigma}^2 - \omega_\sigma \zeta_\sigma^2)
where \zeta are the normal coordinates related to the original...
I was wondering if someone could help me with Goldstein's equation 6.3 (3rd Edition). It is the chapter of oscillations and all that he has done in the equation is to expand it in the form of a Taylor series. I can't seem to get how all those ni's come to get there.