Notes for AKT-140110/0:35:38
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Lagrangian Mechanics is a tool used in studying motions in Classical Mechanics and it was introduced by Joseph-Louis Lagrange in 1788. An important concept in Lagragian Mechanics is that the equations of motion of Classical Mechanics can be based on a variational principle, namely, that along a path describing classical motion the action integral assumes a minimal value (Hamiltonian Principle of Least Action)
The action integral is given by [math]\displaystyle{ S[x(t)] = \int^{t_1}_{t_0} dt \mathcal{L}(x(t),x^\prime(t),t) }[/math], where [math]\displaystyle{ \mathcal{L}(x(t),x^\prime(t),t) = \frac12 {x^\prime(t)}^2-U(x(t)) }[/math] is called the Lagrangian.
