Lagrangian Formalism
A formulation of classical mechanics where system dynamics are derived from a single scalar function, the Lagrangian L(q, q̇, t).
Governing formula
L = T - V (Kinetic Energy minus Potential Energy)
SI unit
Joules (Action S in J·s)
In depth
Formulated by Joseph-Louis Lagrange in 1788. Operates in generalized coordinates q_i, eliminating constraint forces automatically and seamlessly handling complex non-Cartesian geometries.
Examples in the real world
Formulating equations of motion for robotic arms and orbital satellite dynamics.