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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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