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 Failed to parse (syntax error): {\displaystyle S[x(t)] = \int^{t_1}_{t_0} dt \mathcal{L}(x(t),\.{x(t)},t)} , where <math>\mathcal{L}(x(t),\.{x(t)},t) = \frac12 \.{x(t)}^2-U(x(t))/math> is called the Lagrangian.