Notes for AKT-140110/0:35:38

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 $S[x(t)]=\int _{t_{0}}^{t_{1}}dt{\mathcal {L}}(x(t),x^{\prime }(t),t)$, where ${\mathcal {L}}(x(t),x^{\prime }(t),t)={\frac {1}{2}}{x^{\prime }(t)}^{2}-U(x(t))$ is called the Lagrangian.