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# Lagrangian Topic

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The Lagrangian {$\oldstyle L$} is the difference {$T - U$} where {$T$} is the kinetic energy of the system and {$U$} is the potential energy of the system.

{$$\Large \mathcal{L} = T - U \tag{Lagrangian}$$}

I have difficulty understanding why there is a minus sign on the {$U$}. The best I can come with is work from conservative forces is equal to the decrease in potential energy {$W = - \Delta U .$} For conservative forces only, {$\Delta T + W = 0,$} or in other words, the total energy in the system does not change. The only place a change in kinetic energy can come from is from the work done by the conservative forces. So {$\Delta T - \Delta U = 0 .$}

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Categories: TheoreticalPhysicsTopics

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